Question

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

• A. Parabola
• B. Hyperbola
• C. Ellipse
• D. Circle

Answer 1

Answer: (A)

Parabola

Answer 2

Let other end is (h, k)

so centre º $\left( \frac{h + 3}{2},\frac{k + 4}{2} \right)$ touching x- axis means

r = $\frac{k + 4}{2}$

So $\frac{k + 4}{2}$= $\sqrt{\left( \frac{h + 3}{2} - 3 \right)^{2} + \left( \frac{k + 4}{2} - 4 \right)^{2}}$

Hence locus is x² – 6x – 16y + 9 = 0

̃ parabola