Hii! I need answer on the given problems below. Thank you! Your solution will be helpful for me. I also have an example below on how to answer it. So you have a reference.

in obtain the differential equations that describes the following family of curves. 1. Al straight lines passing through ( 2 , -4 ) Equation: point - slope formula y - y . = m ( x - x . ) Characteristic : X1 = 2 , 4. =-4 Arbitrary constant : m 4 +4 = m ( x - 2 ) derive ( , y' = m y + 4 = y ' ( x - 2 ) 2. All cricircles w/ center on the x-axis Equation : C Chik ) ( x - h ) 2 + ( y - k ) 2 = r 2 Characteristic : K = 0 ( because the center is only in x-axis so the distance afrom center upward is o ) Arbitrary constant : rih 1 ( x - h ) 2 + y z = r ( 2 ( x - h ) + zyy ' = 0 ) z @ *h t y y' = o Ityy " ty ly' 20 - Ityy " + (:12 0CIRCLES: DISTANCE: Center at origin. Distance between two points x2 + y2 =2 d2 = (x2- x1)2 + (12- y1)2 Center at point (h, k) Distance between a point and a (x - h)2+ (y- k)? =12 line PARABOLAS: d = [Ax + By + CI/(43 + 83)1/z Axis parallel to x - axis with vertex LINES: at origin Slope - intercept formula yz = + 4ax y = mx +b Axis parallel to x - axis with vertex at (h, k) Point - slope formula (y - k)? = = 4a(x - h) y - y1 = m (x - x1) Axis parallel to y - axis with vertex Two - point form at origin y2 - y1 = m (x2 - x1) x2 = 1 4ay General form Axis parallel to y - axis with vertex Ax + By + C-0 at (h, k) (x - h)? = + 4a(y - k)Steps 1. Identify the equation that you'll use. 2. Apply characteristic. 3. Count the arbitrary constant. 4. Eliminate the arbitrary constant. - Obtain the differential equation that describes the following family of curves. [U 4. All parabolas with axis parallel to x-axis and with distance from the vertex to focus fixed as a. 5. All confocal central conics, with a and b held fixed, 332 3,2 _ :1 a2+A+b2+A