Question

The locus of the centre of a circle which cuts orthogonally the parabola $y^2=4x$ at $(1,2)$ will pass through points

• A. $(3,4)$
• B. $(4,3)$
• C. $(5,3)$
• D. $(2,4)$

Answer 1

The correct option is A $(3,4)$

Tangent at $(1,2)$ to the parabola $y^2=4x$ is
$2y=2(x+1)$
$y=x+1$
It's given that circle cuts the parabola orthogonally.
So, the tangent to the circle at point of intersection is perpendicular to tangent of parabola or the tangent to parabola is a normal to the circle.
Hence, it must pass through the center of the circle.
Center of circle lies on $y=x+1$
Only option A satisfies the above condition.