Question

find the eqn of the locus of a point, the sum of whose distances from (0,2) nd (0,-2) is 6...​

Answer 1

Step-by-step explanation:

You will see the two point (0,2) and (0,-2). Lie on y-axis. From the given condition we find ,if P is a point on the conic , F,F' be the two points (called foci) and PF+PF'=6(a constant). Using this PF+PF'=6=2a(ellipse property), we find a=3. Discover that (0,3) and (0,-3) are vertices. Using relation F(0,ae)=(0,2) we find e=2/3, and b^2=a^2(1-e^2),we get b=5. Therefore the ellipse is x^2/9 +y^2/25 =1.