First slide

Parabola

Question

$If 2 x + y + λ = 0 is a normal to the parabola y^{2} = - 8 x, then λ is$

Moderate

A

12
B

-12
C

24
D

-24

Solution

$y = m x + c is a normal to y^{2} = 4 a x if c = - 2 a m - a m^{3}, y = - 2 x - λ$
$\begin{array}{l} ∴ m = - 2, a = - 2 \\ or - λ = - 2 a m - a m^{3} = - 2 (- 2) (- 2) - (- 2) (- 2)^{3} = - 24 \end{array}$
$or λ = 24$

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