Finding the Vertices of an Ellipse Given Its Foci and a Point on the EllipseThe question is as follows:The focal points of an ellipse are (12,0) and (-12,0), and the point (12,7) is on the ellipse. Find the points where this curve intersects the coordinate axes.I know that the center of the ellipse would be (0,0) because that is the midpoint of the foci. However, I am not sure as to how this information will help me in finding the intersections on the coordinate axes (or the vertices). Any help will be greatly appreciated.

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spornya1 · Accepted Answer

Step 1The 7 in y coordinate of (12,7) is 7, the length of semi-latus rectum; Also c is 12 and       c    2    =  144  =      a    2    −      b    2  . So we have two equations      b    2        /    a  =  7  ,        a    2    −      b    2    =  144  →      a    2    −  7  a  −  144  =  (  a  −  16  )  (  a  +  9  )  =  0Step 2The ends of the required ellipse are at   (  ±  16  ,  0  ) on x-axisThe ends of the (not asked for) hyperbola are at   (  ±  9  ,  0  )  .

The focal points of an ellipse are (12, 0) and (-12, 0), and the point (12, 7) is on the ellipse. Find the points where this curve intersects the coordinate axes.

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