First slide

Parabola

Question

$If PQ is the focal chord of parabola y^{2} = - x and P is (- 4, 2), then the slope of tangent at Q is$

Easy

A

2
B

3
C

4
D

5

Solution

$\begin{array}{l} y^{2} = - x \\ \Rightarrow 2 y \frac{dy}{dx} = - 1 \\ ∴ Slope of tangent at P, {(\frac{dy}{dx})}_{(- 4, 2)} = \frac{- 1}{4} \\ s l o p e o f n o r m a l a t P = 4 \\ \Rightarrow Slope of tangent at Q = 4 (\sin c e \tan g e n t a t o n e e n d o f f o c a l i s p a r a l l e l t o t h e n o r a l a t t h e o t h e r e n d) \end{array}$

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