If one end of a focal chord AB of the parabola y^2=8x is at A1/2,-2, then the equation of the tangent to it at B is:

Correct answer: (B) x-2y+8=0. Let 1/2,-2 is 2t^2,4t⇒t=-1/2 Parameter of other end of focal chord is t=2 ⇒ Point is 8,8 ⇒ Equation of tangent is 8y-4x+8=0 ⇒2y-x=8

Q35 / 75 · JEE Main 2020 (09 Jan Shift 2) · Mathematics

If one end of a focal chord $A B$ of the parabola $y^{2} = 8 x$ is at $A (\frac{1}{2}, - 2),$ then the equation of the tangent to it at $B$ is:

A
$2 x + y - 24 = 0$
Correct answer
B
$x - 2 y + 8 = 0$
C
$x + 2 y + 8 = 0$
D
$2 x - y - 24 = 0$

Solution

Let

(\frac{1}{2}, - 2)

(2 t^{2}, 4 t) \Rightarrow t = - \frac{1}{2}

Parameter of other end of focal chord is $t = 2$

$\Rightarrow$ Point is $(8, 8)$

$\Rightarrow$ Equation of tangent is $8 y - 4 (x + 8) = 0$

$\Rightarrow 2 y - x = 8$

Hence, the correct answer is option: 'B'.

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Solution

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