If the line y = -x + k is a normal to the curve y2 =16x , then k = ____

Equation of normal to the parabola y2 = 4ax having slope m is y = mx - 2am - am3y = -x + k is a normal to the parabola y2 = 16x ⇒m = -1∴k=−2am−am3=−2(4)(−1)−4(−1)3=8+4=12

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If the line y = -x + k is a normal to the curve y² =16x , then k = ____

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answer is 12.

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Detailed Solution

Equation of normal to the parabola y² = 4ax having slope m is y = mx - 2am - am³
y = -x + k is a normal to the parabola y² = 16x $\Rightarrow$ m = -1
$∴ k = - 2 am - {am}^{3} = - 2 (4) (- 1) - 4 (- 1)^{3} = 8 + 4 = 12$