The point (10,26) is a focus of a non-degenerate ellipse tangent to the positive x and y axes. The locus of the center of the ellipse lies along a line. Find the equation of this line.
(In reply to
Answer with incomplete proof by Jer)
I asked for a grid and plotted the line y=(5/13)x+(144/13), per Jer's comment. I took a couple of random points on that line and, for each one, constructed another point on the line connecting (10,26) to the given point and extended that the same distance to get the other focus for the case of the given random center. I then used the ellipse-construction tool to adjust the point that's to go through the ellipse until the ellipse was tangent to the x-axis.
In both cases of the random centers (and resulting foci), the ellipse was also tangent to the y-axis, thus confirming that the centers of such ellipses lie on the line given by Jer.
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Posted by Charlie
on 2024-12-15 20:09:02 |
re: Answer with incomplete proof --- GSP Verification
