If A be a point on the ellipse x^2/a^2 + y^2/b^2 = 1 and B be a point on its auxillary circle vertically above it, then find the locus of the midpt of A,B

Question

anonymous · Answer

The equation for the auxiliary circle is x^2+y^2=a^2

anonymous · Answer

i want that locus
even i know the aux circle

anonymous · Answer

Don't be smart-a## to someone trying to help.

anonymous · Answer

k sorry...cmon..

anonymous · Answer

Some how related to Kepler's laws of planetary motion. Find the radius of the ellipse, radius of the aux: they form two legs of a right triangle. The distance between A, B is hypotenuse.

anonymous · Answer

im getting that but m still nowhere close 2 getting the locus..thnx anyway..

anonymous · Answer

I find that a=b and the distance AB is$$\sqrt{a ^{2}+b ^{2}}$$If you draw the ellipse on an x-y coordinate, you find that x is length a and y is length b, similarly the aux is equal to a. Once again a and b are legs of the right triangle.

anonymous · Answer

the locus is - $$y^2(a^2-b^2) = 0$$
if a point lies on two curves then the locus of the point is the elimination of the equations of the curves.
You have $$x^2b^2 + y^2a^2 = a^2b^2$$ and $$x^2+y^2=a^2$$
solve them up!

anonymous · Answer

no uve got it wrong man..i need the locus of the midpnt of the two points

anonymous · Answer

ahh.. i realise my mistake. I'll try again and let you know