The line y -2 x - k is a normal to the parabola y 2-4 x then k -A- -12B- 10C- -10D- 12

The correct option is A 12y = 2x + k ⇒ 2x – y + k = 0. Here l = 2, m = –1, n = k and a = 1 y = 2x + k is a normal to y^2=4x ⇒ al^2 +2al m^2+m^2n=0 ⇒ 1(2 ...

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Standard XII

Mathematics

Equation of Normal When Slope Is Given

The line y =2...

Question

The line y = 2x + k is a normal to the parabola $y^{2} = 4 x$ then k =

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-12

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-10

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Solution

The correct option is B -12
$y = 2 x + k \Rightarrow 2 x - y + k = 0. H e r e l = 2, m = - 1, n = k a n d a = 1$
$y = 2 x + k i s a n o r m a l t o y^{2} = 4 x \Rightarrow a l^{2} + 2 a l m^{2} + m^{2} n = 0$
$\Rightarrow 1 (2)^{3} + 2 (1) (2) (- 1)^{2} + k = 0 \Rightarrow k + 12 = 0 \Rightarrow k = - 12$

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The line y = 2x + k is a normal to the parabola y2=4x then k =

The correct option is B -12y=2x+k⇒2x–y+k=0.Here l=2,m=–1,n=k and a=1 y=2x+k is a normal to y2=4x⇒al2+2alm2+m2n=0 ⇒1(2)3+2(1)(2)(−1)2+k=0⇒k+12=0⇒k=−12

The line y = 2x + k is a normal to the parabola $y^{2} = 4 x$ then k =