The sum of the squares of the distances of a moving point from two fixed points (a,0) and `(-a ,0)` is equal to a constant quantity `2c^2dot` Find the

Question

The sum of the squares of the distances of a moving point from two fixed points (a,0) and `(-a ,0)` is equal to a constant quantity `2c^2dot` Find the

The sum of the squares of the distances of a moving point from two fixed points (a,0) and `(-a ,0)` is equal to a constant quantity `2c^2dot` Find the equation to its locus.

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

If the sum of three numbers which are in A.P is 15 and the sum of the squares of the extremes is 58, then those numbers are

2 Answers 5 Views

If the squares of a `8 xx 8` chess board are painted either red and black at random .The probability that not all squares is any alternating in colour

2 Answers 9 Views

If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.

2 Answers 4 Views

Find the locus of a point, the sum of squares of whose distance from the planes `x-z=0,x-2y+z=0a n dx+y+z=0i s36` .

2 Answers 4 Views

Find the locus of appoint which moves such that the sum of the squares of its distance from the points `A(1,2,3),B(2,-3,5)a n dC(0,7,4)i s120.`

2 Answers 11 Views

Let points A,B and C lie on lines y-x=0, 2x-y=0 and y-3x=0, respectively. Also, AB passes through fixed point P(1,0) and BC passes through fixed point

2 Answers 11 Views

Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three point out of these lie on a

2 Answers 7 Views

The intensities of magnetic field at two points on the axis of a bar magnet at distances 0.1m and 0.2 m from its middle point are in the ratio 12.5:1.

2 Answers 20 Views

The intensities of magnetic field at two points on the axis of a bar magnet at distances `0.1` m and `0.2` m from its middle point are in the ratio `1

2 Answers 6 Views

Just as large distances are measured in AU, parsec or light year, atomic or nuclear distances are measured with the help of microscopic units.

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Let `P(h,k)` be any position of the moveing point and let `A(a,0), B(-a,0)` be the given points. Then, we have `PA^2+PB^2=2c^2` (Given)
or `(h-a)^2+(k-0)^2+(h+a)^2+(k-0)^2=2c^2`
`2h^(2)2k^2+2a^2=2c^2`
or `h^2+k^2=c^2-a^2`
Hence, the equation to locus `(h,k)` is `x^2+y^2 =c^2-a^2`.

4 views Answered 2023-02-05 15:29