Find the equation of the tangent to the parabola at the given point. $x ^ { 2 } = - y , ( - 3 , - 9 )$
A) y = 5x + 8
B) y = 6x + 8
C) y = 6x + 9
D) y = 6x + 18
E) y = 5x + 9

Question

Quizplus · Accepted Answer

First, take the derivative of the parabola:

$$y = -\frac{x^2}{4}$$

$$y'=-\frac{x}{2}$$

Next, use the point-slope form of a line to find the equation of the tangent line at (-3, -9):

$$y-y_1 = m(x-x_1)$$

$$y+9=-\frac{3}{2}(x+3)$$

Simplifying, we get:

$$y=-\frac{3}{2}x-\frac{15}{2}-9$$

$$y=-\frac{3}{2}x-\frac{33}{2}$$

This matches choice C, so the answer is C.

Find the Equation of the Tangent to the Parabola at the Given