Exam

JEE Main

Year

2019

Date

11 January

Shift

Evening Shift

Subject

Mathematics

Chapter

Circle

JEE Main 2019 · 11 January · Evening Shift · Mathematics · Circle

A circle cuts a chord of length 4 a on the x -axis and passes...

A circle cuts a chord of length 4 a on the $x$ -axis and passes through a point on the $y$ -axis, distant $2 \mathrm{~b}$ from the origin. Then the locus of the centre of this circle, is:

Step-by-step solution

Let centre be $C(h, k)$ $C Q=C P=r$ $\Rightarrow C Q^{2}=C P^{2}$ $(h-0)^{2}+(k \pm 0)^{2}=C M^{2}+M P^{2}$ $h^{2}+(k \pm 2 \mathrm{~b})^{2}=k^{2}+4 a^{2}$ $h^{2}+k^{2}+4 b^{2} \pm 4 b k=k^{2}+4 a^{2}$ Then, the locus of centre $C(h, k)$ $x^{2}+4 b^{2} \pm 4 b y=4 a^{2}$ Hence, the above locus of the centre of circle is a parabola.