The centre of the circle passing through the point and touching the curve at is
Explanation for the correct option:
Finding the center of the circle:
The general equation of the circle is .
Given, the circle passes through point .
Substitute and in equation .
Substitute the value of in equation .
So, equation of circle become
Circle also passes through , that means this point satisfy the circle.
Substitute and .in equation .
The center of the circle should satisfy equation .
Checking for Option (C).
Option (C) satisfies the equation.
Explanation for the incorrect option :
For Option (A),
since the equation is not satisfied, it is incorrect.
For Option (B),
since the equation is not satisfied, it is incorrect.
Therefore, the correct answer is option (C).