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Prove that the equation of the parabola ...

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is `x-y+1 = 0 ` is `x^2 + y^2 + 2xy - 4x + 4y - 4=0`.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
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  14. Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

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