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JEE Main 20209 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Parabola

JEE Main 2020 · 9 January · Evening Shift · Mathematics · Parabola

If one end of a focal chord AB of the parabola y ^ 2 = 8x is at...

If one end of a focal chord

AB

of the parabola

{y}^{2} = 8x

is at

A\left(\dfrac{1}{2}, - 2\right), then the equation of the tangent to it at

B$ is:

Options

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

Correct answer

B. $x - 2y + 8 = 0$

Step-by-step solution

Let

\left(\dfrac{1}{2}, - 2\right)

is \left(2{t}^{2}, 4t\right) ⇒ t = - \dfrac{1}{2}

<p>Parameter of other end of focal chord is

t = 2

</p><p>

⇒

Point is \left(8, 8\right)

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

$⇒ 2y - x = 8$

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