Tangents are drawn to the parabola y2=4 x at the point P which is the upper end of latus rectum. Image of the parabola y2=4 x in the tangent line at the point P is

Question

Tangents are drawn to the parabola y2=4 x at the point P which is the upper end of latus rectum. Image of the parabola y2=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)

Tardigrade Admin · Accepted Answer

text Point P text is (1,2) text Tangent is 2 y =2( x +1) text i.e. y = x +1 hence image of y2=4 x in (2) can be written as (x+1)2=4(y-1) ⇒ text (C)

Q. 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

$(x + 4)^{2} = 16 y$

$(x + 2)^{2} = 8 (y - 2)$

$(x + 1)^{2} = 4 (y - 1)$

$(x - 2)^{2} = 2 (y - 2)$

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

Q. Tangents are drawn to the parabola y2=4x at the point P which is the upper end of latus rectum. Image of the parabola y2=4x in the tangent line at the point P is

(x+4)2=16y

(x+2)2=8(y−2)

(x+1)2=4(y−1)

(x−2)2=2(y−2)