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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 PUBLICATION-CONIC SECTIONS-All Questions
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  2. The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q...

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  3. Prove that the equation of the parabola whose focus is (0, 0) and tang...

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  4. The equation of the parabola whose vertex and focus lie on the axis of...

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  6. Two parabola have the same focus. If their directrices are the x-and t...

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  7. The number of common chord of the parabolas x=y^(2)-6y+11andy=x^(2)-6x...

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  8. Find the equation of the curve whose parametric equations are x=1+4c...

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  9. Prove that any point on the ellipse whose foci are (-1,0) and (7,0)...

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  10. Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=...

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  11. Find the area of the greatest rectangle that can be inscribed in an ...

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  12. The auxiliary circle of a family of ellipses passes through the ori...

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  13. Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

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  14. A line passing through the origin O(0,0) intersects two concentric ...

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  15. If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2)...

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  16. Find the maximum area of an isosceles triangle inscribed in the ellips...

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  17. Find the eccentric angles of the extremities of the latus recta of ...

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  18. Find the equation of the ellipse whose axes are of length 6 and 2sq...

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  19. If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 repr...

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  20. Obtain the equation of the ellipse whose focus is the point (-1, 1), a...

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