The correct option is
C (0,−1)The given equation of the parabola is
y2=4x4ax=4xa=1
Equation of latus rectum is x=1
Putting x=1 in equation of parabola
we get
y2=4y=±2
Hence end point of latus rectum are (1,2),(1,−2)
Now equation of parabola is
y2=4x
Differentiating on both sides with respect tox
$2y\cfrac{dy}{dx}=4\\ \Rightarrow\cfrac{dy}{dx}
=m=\cfrac{4}{2y}$
At y=2m=1
At y=−2am=−1
The equation of tangent is given by
(y−y1)=m(x−x1)
At (1,2)
⇒y−2=1(x−1)⇒y=x+1
At (1,−2)y+2=−1(x−1)y=−x−1
Intersection point of two tangent will be
−x−1=x+1⇒2x=−2⇒x=−1
Now, y=−x−1⇒y=1−1⇒y=0
Hence, intersection point (−1,0) lies on direction x=−1