Question

Find the locus of a point such that the
sum of its distance from the points
(o,2) and (0-2) is 6​

Answer 1

The locus of points, whose sum of distance from two fixed points is constant is an ellipse.

For ellipse, x^2/b^2 + y^2/a^2 =1

Here, the constant sum 2a=6 or a=3

And distance between focii (0,2) and (0,−2) is 4

2ae=4 or e=2/3

Since the focii lie on the y axis, the equation of the ellipse will be of the form x^2/a^2(1-e^2) +

y^2/a^2 =1

x^2/9 (1-4/9) +y^2/9 =1

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