Question

a line is drawn from the origin to a point on the ellipse 9x^2+25y^2=225.find the equation of the locus of midpoint of the line.

Answer 1

a point (x,y) on the ellipse is
(x,(1/5)√(225-9x^2))

halfway there is

(x/2,(1/10)√(225-9x^2))

x^2/4 + y^2/b^2 = 1
x^2/4 + (225-9x^2)/100b^2 = 1
25b^2x^2/4 + 225-9x^2 = 100b^2
(25b^2/4 - 9)x^2 = 100b^2-225
25b^2/4 = =9
b^2 = 36/25

x^2/4 + (25/36)y^2 = 1
9x^2 + 25y^2 = 36

Hmmm. Not what I expected. 36 seems too small. Better check the distance of the two points on some radius.