JEE PYQ: Parabola Question 14
Question 14 - 2020 (09 Jan Shift 2)
If one end of a focal chord AB of the parabola $y^2 = 8x$ is at $A\left(\frac{1}{2}, -2\right)$, then the equation of the tangent to it at $B$ is:
(1) $2x + y - 24 = 0$
(2) $x - 2y + 8 = 0$
(3) $x + 2y + 8 = 0$
(4) $2x - y - 24 = 0$
Show Answer
Answer: (2)
Solution
$y^2 = 8x$, $a = 2$. $A = (2t_1^2, 4t_1) = \left(\frac{1}{2}, -2\right) \Rightarrow t_1 = -\frac{1}{2}$. Other end: $t_2 = -\frac{1}{t_1} = 2$. $B = (8, 8)$. Tangent at $B$: $8y - 4(x+8) = 0 \Rightarrow 2y - x = 8 \Rightarrow x - 2y + 8 = 0$.
BETA
