AP EAMCET · Maths · Ellipse
The sum of the squares of the distances of a moving point from 2 fixed points \(A(a, 0)\) and \(B(-a, 0)\) is equal to a constant \(2 c^2\), then the equation of its locus is
- A \(x^2+y^2=c^2-a^2\)
- B \(x^2+y^2=c^2+a^2\)
- C \(2 x^2+2 y^2=c^2+a^2\)
- D \(2 x^2-2 y^2=c^2+a^2\)
Answer & Solution
Correct Answer
(A) \(x^2+y^2=c^2-a^2\)
Step-by-step Solution
Detailed explanation
Let the point be \(P(x, y)\). Then, \[ \begin{aligned} & B P=\sqrt{(x+a)^2+(y-0)^2} \\ & \text { and } A P=\sqrt{(x-a)^2+(y-0)^2} \end{aligned} \] Given that, \[ (B P)^2+(A P)^2=2 c^2 \] i.e. \((x+a)^2+y^2+(x-a)^2+y^2=2 c^2\)…
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