Question

$y=3 x-2$ is a straight line touching the parabola $(y-3)^{2}=12(x-2)$. If a line drawn perpendicular to this line at $P$ on it, touches the given parabola, then the point $P$ is

• A. $(-1,-5)$
• B. $(-1,5)$
• C. $(-2,-8)$
• D. $(2,4)$

Answer 1

Answer: (A)

According to the given information, Angle between the tangents is $90^{\circ} .$
$\Rightarrow $ The point on the directrix
Here, $x-2=-3$
$x=-1$ is directrix
Given tangent is $y=3 x-2$
$\therefore y=3(-1)-2=-5$
$\therefore $ Point $P$ is $(-1,-5)$