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

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Ans: (A)

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.