SOLUTION: If the focci of ellipse is {{{ x^2/9 + y^2/4 = 1 }}} subtend a right angle at some point P. Find the locus of point P?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: If the focci of ellipse is {{{ x^2/9 + y^2/4 = 1 }}} subtend a right angle at some point P. Find the locus of point P?      Log On


   

Question 1184288: If the focci of ellipse is +x%5E2%2F9+%2B+y%5E2%2F4+=+1+ subtend a right angle at some point P. Find the locus of point P?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The foci of the ellipse  x%5E2%2F9 + y%5E2%2F4 = 1  are the points  (-c,0)  and  (c,0)  on  x-axis,  where c = sqrt%289-4%29 = sqrt%285%29.



The locus of points P such that the foci subtend the right angle at point P is the circle, 

centered at the origin of the coordinate plane  and having the radius of  sqrt%285%29,  EXCLUDING

the endpoints of its diameter that lie on x-axis.

Solved, answered and explained.