Question

***1. Find the equation of locus of a point, the
difference of whose distances from (-5, 0) and
(5, 0) is 8.
​

Answer 1

Step-by-step explanation:

Let coordinates of P (h,k), Acordingly:-

PA+PB=6

PA= 6-PB

or. PA^2=36+PB^2-12PB

or. 12.PB=36+PB^2-PA^2

or. 12.PB=36+h^2+(k+2)^2-h^2-(k-2)^2

or. 12.PB=36+8k

or. 3.PB=9+2k

or. 9.PB^2=81+36k+4k^2

or. 9[(h-0)^2+(k+2)^2]=81+36k+4k^2

or. 9h^2+9k^2+36k+36 =81+36k+4k^2

or. 9h^2+5k^2=45

Locus of (h,k) is:-

9x^2+5y^2= 45.