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dajugganaut

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Hi all. I have a analytic geometry question that I need a bit of help with.

consider the concentric circles with the equations:

[tex]x^2 + y^2 = 9[/tex]

and

[tex]x^2 +y^2 = 4[/tex]

A radius from the center O intersects the inner circle at P and the outer circle at Q. The line parallel to the x-axis through P meets the line parallel to the y-axis through Q at the point R. Prove that R lies on the ellipse

[tex]((x^2)/9) + ((y^2)/4) =1[/tex]

Some of the facts I've established:

the distance from P to Q is 1 for sure. Also, the triagle PQR is a right angle triangle. using the ellipse equation, i know that the distance from the center to the vertex is 3, and that the distance from the center to the focus is the square root of 5.

consider the concentric circles with the equations:

[tex]x^2 + y^2 = 9[/tex]

and

[tex]x^2 +y^2 = 4[/tex]

A radius from the center O intersects the inner circle at P and the outer circle at Q. The line parallel to the x-axis through P meets the line parallel to the y-axis through Q at the point R. Prove that R lies on the ellipse

[tex]((x^2)/9) + ((y^2)/4) =1[/tex]

Some of the facts I've established:

the distance from P to Q is 1 for sure. Also, the triagle PQR is a right angle triangle. using the ellipse equation, i know that the distance from the center to the vertex is 3, and that the distance from the center to the focus is the square root of 5.

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