JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 center of this circle, is
- A a hyperbola
- B an ellipse
- C a straight line
- D a parabola
Answer & Solution
Correct Answer
(D) a parabola
Step-by-step Solution
Detailed explanation
\({k^2} + 4{a^2} = {r^2}\) and \({\left( {h - 0} \right)^2} + {\left( {k - 2b} \right)^2} = {r^2}\) \( \Rightarrow {h^2} + {\left( {k - 2b} \right)^2} = {k^2} + 4{a^2}\) \( \Rightarrow {h^2} + 4bk - 4{b^2} + 4{a^2}\) Locus is \({x^2} = 4\left( {by - {b^2} + {a^2}} \right)\)…
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