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# Fp3 elipses question help

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One method:

Consider a point on the ellipse, and a line of gradient m going through that point; so, get the equation of that line.

You now need to find the other point of intersection with the ellipse and the midpoint of the two. So, sub the y= of the line into the equation of the ellipse to get a rather horrendous quadratic. It will have two roots; being the x-coordinate of the two points of intersection.

Note: If you're clever about it you don't need to actually find the second point. Think about what you want to find, and how it relates to the equation and its roots.

Having worked out the coordinates of the midpoint, show that they lie on a line.

I get

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