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Prove that the equation `y^2+2ax+2by+c=0` represent a parabola whose axis is parallel to the axis of x. Find its vertex.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Find the equations of the parabola with vertices at the origin and sat...

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  2. Find the equation of the parabola whose latus-rectum is 4 units , axis...

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  3. Prove that the equation y^2+2ax+2by+c=0 represent a parabola whose ax...

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  4. Find the equation of the parabola which is symmetric about y-axis and ...

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  5. Find the foci, vertices, directrices, and axes of following parabola. ...

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  6. Find the foci, vertices, directrices, and axes of following parabola. ...

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  7. Find the foci, vertices, directrices, and axes of following parabola. ...

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  8. Find the vertex, focus, latus-rectum, axis and directrix of the parabo...

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  9. Find the vertex, axis, focus and directrix of the parabola x^2+ 4x + 2...

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  10. Find the focus, vertex, equation of the directrix and the axis of the ...

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  11. Find the area of the triangle formed by the lines joining the vertex o...

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  12. Find the equation of the parabola whose focus is (1, 1) and tangent at...

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  13. Show that the area of the triangle inscribed in the parabola y^2= 4ax ...

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  14. The focus of a parabolic mirror as shown in the figure is at a distanc...

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  15. The cable of a uniformly loaded suspension bridge hangs in the form of...

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  16. A water jet from the fountain reaches its maximum height of 4 metres a...

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  17. A beam is supported at its end points by supports which are 12 metres ...

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  18. If the eccentricity is zero, show that the ellipse becomes a circle.

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  19. Find the equation of the ellipse with foci at (+-5 ,0) and x=36/5 as o...

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  20. Find the lengths of the major and minor axes, the co-ordinates of the ...

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