Question

If a circle whose one end of the diameter is focus of the parabola $y^2=4x$ and other end is a point on parabola, then which of the following line will always be a tangent to the given circle?

• A. $x=0$
• B. $x=-1$
• C. $x=1$
• D. $y=0$

Answer 1

The correct option is A $x=0$

Given parabola $y^2=4x$

One end of diameter is $(1,0)$ (the focus) and other end lies on the parabola.
Hence circle is drawn on semi focal length as diameter so it has to touch the tangent at vertex i.e. $x=0$