Question

Tangents are drawn to the parabola $y^2=4 x$ at the point $P$ which is the upper end of latus rectum.
Image of the parabola $y^2=4 x$ in the tangent line at the point $P$ is

• A. $(x+4)^2=16 y$
• B. $( x +2)^2=8( y -2)$
• C. $( x +1)^2=4( y -1)$
• D. $(x-2)^2=2(y-2)$

Answer 1

Answer: (C)

$\text { Point } P \text { is }(1,2) $
$\text { Tangent is } 2 y =2( x +1) $
$\text { i.e. } y = x +1$
hence image of $y^2=4 x$ in (2) can be written as
$(x+1)^2=4(y-1) \Rightarrow \text { (C) }$