NDA Maths Mock Test – 01 – Q58

The sum of the squaresof the distances of a moving point from two fixed points (p, 0) and (-p, 0) is equal to a constant quantity 2λ² , find the equation of the locus.

• x² + y² = lambda² + p²
• x² + y² = lambda² – p²
• x² – y² = lambda² – p²
• x² – y² = lambda² + p²

Let P(h, k) be any position of the mo√ing point and A(p, 0), B(-p, 0) be the gi√en points.
‘ Then,
‘ PA? + PB? = 2)?
= (h=p)? + (k= 0)2+(h +p)? + (k— 0)? =2)2
‘ = h? — 2ph +p? + K? + h2+2ph + p? + K2 = 2X2
hon a
‘ = 2h% + 2k? + 2p? = x² ‘
= h? +k? =\ —p?
.
Hence, the locus of (h, k) is 2% + y? = A? — p².