Question

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

• A. A hyperbola
• B. A parabola
• C. A straight line
• D. An ellipse

Answer 1

Answer: (B)

A parabola

Answer 2

Let equation of circle is $x^2 + y^2 + 2fx + 2fy +e = 0 ,$ it passes through $(0, 2b)$
$\Rightarrow \; 0 + 4b^2 + 2g \times 0 + 4? + c = 0$
$\Rightarrow \; 4b^2 + 4f + c = 0$ ...(i)
$2 \sqrt{g^2 -c} = 4a$ ....(ii)
$g^2 - c = 4a^2 \; \Rightarrow \; c = (g^2 - 4a^2)$
Putting in equation (1)
$\Rightarrow \; 4b^2 + 4f + g^2 - 4a^2 = 0$
$\Rightarrow \; x^2 +4y +4 (b^2 -a^2) = 0$ it represent a parabola.