Question: Let P(3, 4) be a point on the circle x2 + y2 = 25 (see figure). (a) What is the slope of the line joining

Let P(3, 4) be a point on the circle x2 + y2 = 25 (see figure).

(a) What is the slope of the line joining P and O(0, 0)?

(b) Find an equation of the tangent line to the circle at P.

(c) Let Q(x, y) be another point on the circle in the first quadrant. Find the slope mx of the line joining P and Q in terms of x.

(d) Calculate lim x→3 mx. How does this number relate to your answer in part (b)?

-6 -2 2 -6+ Figure for 4 2 P(3, 4) Q 6

X 

-6 -2 2 -6+ Figure for 4 2 P(3, 4) Q 6 X

Step by Step Solution

★★★★★

3.48 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a The slope of the line joining P34 and O00 is m y2 y1x2 x1 0 40 3 43 b To find the equation of the ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Restaurants have traditionally used bottom-end wines to sell by the glass (BTG) at reasonably low prices per glass. In recent years, there has been a growing trend within the restaurant industry to...

Q:

Let P(5, 12) be a point on the circle x 2 + y 2 = 169 (see figure). (a) What is the slope of the line joining P and O(0, 0)? (b) Find an equation of the tangent line to the circle at P. (c) Let Q(x,...

Q:

Let P(a, b) be a point on the first quadrant portion of the curve y = 1/x and let the tangent line at P intersect the x-axis at A. Show that triangle AOP is isosceles and determine its area.

Q:

caps lock X C Z shift alt Figure 21. 22. Match the functions (a)-(d) with their contour maps (A)-(D) in (a) f(x, y) = 3x + 4y (c) h(x, y ) = 4x - 3y (b) 8 (x, y ) = x3 - y (d) k (x, y) = x2 - y 104...

Q:

1. Find the slope of the line segment from P:( x,x2 + x) Q=(a,a2 + a) fora-#3:. 2. Find the distance (that is, the shortest distance) from the point (1, 8) to the line L : 3y- x : 3. 3. Find an...

Q:

15. [l0.33 Points] DETAILS SPRECALC'I 2.1.062.Ml. 0/5 Submissions Used Find the domain of the function. (Enter your answer using interval notation.) F(X)=\\/29x Need Help? MY NOTES ASK YOUR TEACHER...

Q:

10. (a) In Figure l, the shaded region is bounded by the circle x2 +y2 = r1, the x-axis and the line y=h,where OShSr. A solid of revolution is formed by revolving the region about the y-axis. {2...

Q:

. Find an equation of the line tangent to the circle x^2 + y^2 = 25 at the point P when: (a) P = (3, 4) (b) P = (4, 3) (c) P = (0, 5) (d) P = (5, 0)

Q:

1.) A 20 foot long pole leans against a wall. The bottom is 12 feet from the wall. How much farther should the bottom be pulled away from the wall so that the top moves the same amount down the wall?...

Q:

878 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES (e) Does P correspond to a minimum or maximum value of f? Re- fer to Figure 12 to justify your answer. Hint: Do the values of f(x, y) 2 increase or...

Q:

Draw structures for these compounds: (a) Diethyl ammonium bromide (b) N-Methyl-3-(1-methylpropyl)-2-octanamine

Q:

Do you think it is necessary to prohibit all of the services on the prohibited services list in order to protect the public interest? Are there any on the list that you would permit, and why?

Q:

Determine the net income ( loss ) for the period. a . Net income is $ 2 7 , 7 7 2 . b . Net income is $ 2 , 1 7 3 . c . Net loss is $ 2 , 1 7 3 . d . Net loss is $ 4 , 9 3 4 .

Q:

(b) What are the ethical considerations of (1) the presidents request and (2) Cathis dating the adjusting entries December 31?

Q:

In Exercises find the second derivative of the function. f(x) = x + 3x-3

Q:

In Exercises find the second derivative of the function. f(x) = = x-1

Q:

In Exercises evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result. g(t) = tan 2t, 3

Q:

ans plz Buyers have different needs that can be addressed by YOU, the salesperson Situational needs Functional needs Social needs Psychological needs Knowledge needs Take two (2) of the above needs,...

Q:

For the year 2018 i need Marias: -1040 -Schedule 1 -Schedule 4 -Schedule 5 -Schedule C -Schedule SE Please provide the correct numbers and properly written for the above forms. All the information is...

Q:

Initial Investment=$8 --> expected to generate $1.1 EBIT in year 1 with a 3% growth rate for perpetuity. Corporate Tax = 35%, Equity Cost of Capital = 13.5%, Debt Cost of Capital = 7% 1. What is the...