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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Find the indicated quantities for each of the given equations. Sketch each curve.2x2 + 2y2 + 4x − 8y − 15 = 0, center and radius
Plot the curves of the given polar equations in polar coordinates.r = 2sinθ tanθ (cissoid)
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.y2 − 2x − 2y − 9 = 0
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Directrix y = 2.3
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Focus (0, 2), passes through (−1, √3)
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Passes through (−2, 2) and (1, √6)
Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph.x2 = 6x − 4y2 − 1
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.2y + 4x − 5 = 0
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Asymptote y = −4x, vertex (0, 4)
Find the slopes of the lines with the given inclinations.62.5°
An elliptical cam can be represented by the equation x2 − 3xy + 5y2 − 13 = 0. Through what angle is the cam rotated from its standard position?
Find the rectangular coordinates for each of the points for which the polar coordinates are given.(−3.0, 3.0)
Find the indicated quantities for each of the given equations. Sketch each curve.8x2 + 2y2 = 2, vertices and foci
Plot the curves of the given polar equations in polar coordinates.r −2r cosθ =6 (hyperbola)
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.4x2 + 9y2 + 24x = 0
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.The difference of distances to (x, y) from (10, 0) and (−10, 0) is 12.
Find the indicated quantities for each of the given equations. Sketch each curve.4x2 − 25y2 = 0.25, vertices and foci
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Passes through (1, 2) and (2, 2√2)
Plot the curves of the given polar equations in polar coordinates.(ellipse) r r = 3 2 - cose
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.4y = 6x − 9
Find the slopes of the lines through the points.(a, h2) and [a + h, (a + h)2]
What is the x´y´ equation of the line y = x when the axes are rotated through 45°.
Find the rectangular coordinates for each of the points for which the polar coordinates are given.(4, −π)
Find the indicated quantities for each of the given equations. Sketch each curve.x2 = −20y, focus and directrix
Determine the center and radius of each circle. Sketch each circle.x2 + (y − 3)2 = 4
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.x2 + 4y = 24
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Axis x = 0, passes through (−1, 8)
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.Passes through (2, 2) and (1, 4)
Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph.x2 = 8(y − x − 2)
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.3x − 2y − 1 = 0
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.Asymptote y = 2x, vertex (1, 0)
Find the slopes of the lines with the given inclinations.30°
What is the x´y´ equation of the function y = 2x when the axes are rotated through 90°?
Find the rectangular coordinates for each of the points for which the polar coordinates are given.(−3.0,−0.40)
Find the indicated quantities for each of the given equations. Sketch each curve.y2 = 0.24x, focus and directrix
Determine the center and radius of each circle. Sketch each circle.4(x + 1)2 + 4(y − 5)2 = 81
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Passes through (3, 5) and (3,−5)
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.The sum of distances from (x, y) to (6, 0) and (−6, 0) is 20.
Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph.y2 = 2(x2 − 2x − 2y)
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.11.2x + 1.6 = 3.2y
Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph.4x2 + 4 = 9 − 8x − 4y2
Reduce the equations to slope-intercept form and find the slope and the y-intercept. Sketch each line.11.5x + 4.60y = 5.98
Find the equations of the hyperbolas satisfying the given conditions. The center of each is at the origin.The difference of distances to (x, y) from (0, 4) and (0,−4) is 6.
Plot the curves of the given polar equations in polar coordinates.r = 4cos 1/2θ
Find the inclinations of the lines with the given slopes0.364
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.9x2 − y2 + 8y = 7
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Passes through (3, 3) and (12, 6)
Determine the center and radius of each circle. Sketch each circle.2x2 + 2y2 − 16 = 4x
Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph.y2 + 42 = 2x(10 − x)
Determine whether the given lines are parallel, perpendicular, or neither.3x − 2y + 5 = 0 and 4y = 6x − 1
Find the rectangular coordinates for each of the points for which the polar coordinates are given.(8.0,−8.0)
Find the indicated quantities for each of the given equations. Sketch each curve.2y2 − 9x2 = 18, vertices and foci
Plot the curves of the given polar equations in polar coordinates.3r − 2r sinθ = 6 (ellipse)
Find the slopes of the lines with the given inclinations.93.5°
Determine the center and radius of each circle. Sketch each circle.4(x + 7)2 + 4(y + 11)2 = 169
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin.The sum of distances from (x, y) to (0, 2) and (0,−2) is 5.
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Passes through (6,−1) and (−6,−1)
Find the rectangular coordinates for each of the points for which the polar coordinates are given.(π, 4.0)
Find any point(s) of intersection of the graphs of the ellipse 4x2 + 9y2 = 40 and the parabola y2 = 4x
Sketch the graph of the hyperbola xy = 2.
Find the polar equation of each of the given rectangular equations.x = 3
Find the indicated quantities for each of the given equations. Sketch each curve.4x2 + 50y2 = 1600, vertices and foci
Plot the curves of the given polar equations in polar coordinates.r = 2 + cos3θ
Find the inclinations of the lines with the given slopes1.903
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.2x2 − 4x = 9y − 2
Find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.Passes through (−5,−5) and (−10,−20)
Determine the center and radius of each circle. Sketch each circle.y2 + x2 − 4x = 6y + 12
Identify the curve represented by each of the given equations. Determine the appropriate important quantities for the curve and sketch the graph.x2 − 4y = y2 + 4(1 − x)
Determine whether the given lines are parallel, perpendicular, or neither.8x − 4y + 1 = 0 and 4x + 2y − 3 = 0
Find the equation of the circle that has the same center as the ellipse 4x2 + 9y2 = 36 and is internally tangent to the ellipse.
Sketch the graph of the hyperbola xy = −4.
Find the polar equation of each of the given rectangular equations.y = −x
Find the indicated quantities for each of the given equations. Sketch each curve.x2 − 8x − 4y − 16 = 0, vertex and focus
Find the inclinations of the lines with the given slopes−6.691
Plot the curves of the given polar equations in polar coordinates.r = 2[1 − sin(θ − π/4)]
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.5x2 − 4y2 + 20x + 8y = 4
At what point(s) do the parabolas y2 = 2x and x2 = −16y intersect?
Determine the center and radius of each circle. Sketch each circle.x2 + y2 + 4.20x − 2.60y = 3.51
Identify the type of curve for each equation, and then view it on a calculator.x2 + 2y2 − 4x + 12y + 14 = 0
Determine whether the given lines are parallel, perpendicular, or neither.6x − 3y − 2 = 0 and 2y + x − 4 = 0
Find the equation of the ellipse with foci (−2, 1) and (4, 1) and a major axis of 10, by use of the definition. Sketch the curve.
Show that the parametric equations x = sec t, y = tan t define a hyperbola.
Find the polar equation of each of the given rectangular equations.x + 2y + 3 = 0
Find the indicated quantities for each of the given equations. Sketch each curve.y2 − 4x + 4y + 24 = 0, vertex and directrix
Find the inclinations of the lines with the given slopes−0.0721
Plot the curves of the given polar equations in polar coordinates.r = 4tanθ
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.0.04x2 + 0.16y2 = 0.01y
Using trigonometric identities, show that the parametric equations x = sint, y = 2(1 − cos2 t) are the equations of a parabola.
Determine the center and radius of each circle. Sketch each circle.2x2 + 2y2 + 44x + 28y = 52
Identify the type of curve for each equation, and then view it on a calculator.4y2 − x2 + 40y − 4x + 60 = 0
Determine whether the given lines are parallel, perpendicular, or neither.3y − 2x = 4 and 6x − 9y = 5
Find the equation of the ellipse with foci (1, 4) and (1, 0) that passes through (4, 4), by use of the definition. Sketch the curve.
Show that all hyperbolas have foci at (±1, 0) for all values of θ. x² cos²0 y² sin ²0 1
Find the polar equation of each of the given rectangular equations.x2 + y2 = 0.81
Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.4x2 − y2 + 32x + 10y + 35 = 0
Find the indicated quantities for each of the given equations. Sketch each curve.4x2 + y2 − 16x + 2y + 13 = 0, center
Determine whether the lines through the two pairs of points are parallel or perpendicular.(6,−1) and (4, 3); (−5, 2) and (−7, 6)
View the curves of the given polar equations on a calculator.r = θ (−20 ≤ θ ≤ 20)
Find the equation of the parabola with focus (6, 1) and directrix x = 0, by use of the definition. Sketch the curve.
Determine the center and radius of each circle. Sketch each circle.4x2 + 4y2 − 9 = 16y

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