If one end of the diameter of a circle is (3, 4) which touches the x-axis then the locus of other end of the diameter of the circle is

Q: If one end of the diameter of a circle is (3, 4) which touches the x-axis then the locus of other end of the diameter of the circle is

(A) parabola

(B) hyperbola

(C) ellipse

(D) none of thee

Sol. Let other end of diameter be (h, k).

Hence Centre is $\large (\frac{3+h}{2} , \frac{4+k}{2}) $

This circle touches x-axis means $ r = \frac{4+k}{2} $

$\large = \sqrt{(\frac{3+h}{2} – 3)^2 + (\frac{4+k}{2}-4)^2}$ gives the equation of parabola (replacing (h, k) by (x, y).

Hence (A) is the correct answer.