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If the parabolas y^(2)=4axandy^(2)=4c(x-...

If the parabolas `y^(2)=4axandy^(2)=4c(x-b)` have a common normal other than x-axis (a,b,c being distinct positive real numbers), then prove that `(b)/(a-c)gt2`.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the locus of midpoint of normal chord of parabola y^(2)=4ax.

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  2. If normal to the parabola y^2-4a x=0 at alpha point intersects the par...

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  3. If the parabolas y^(2)=4axandy^(2)=4c(x-b) have a common normal other ...

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  4. Find the angle made by a double ordinate of length 8a at the vertex of...

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

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  6. If the chord of contact of tangents from a point P to the parabola y^2...

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  7. Tangents are drawn from any point on the line x+4a=0 to the parabola y...

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  8. If a normal to a parabola y^2 =4ax makes an angle phi with its axis, t...

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  9. Tangents are drawn to y^(2)=4ax at point where the line lx+my+n=0 meet...

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  10. Find the vertex of the parabola x^2=2(2x+y).

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  11. Find the length of the common chord of the parabola y^2=4(x+3) and th...

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  12. Find the coordinates of any point on the parabola whose focus is (0, 1...

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  13. If the focus and vertex of a parabola are the points (0, 2) and (0, 4)...

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  14. Find the length of the latus rectum of the parabola whose focus is at ...

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  15. The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the eq...

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  16. The vertex of a parabola is (2,2) and the coordinates of extremities o...

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  17. Find the equation of the directrix of the parabola x^2-4x-3y+10=0.

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  18. Find the locus of midpoint of chord of the parabola y^(2)=4ax that pas...

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  19. In the parabola y^(2)=4ax, the tangent at P whose abscissa is equal to...

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  20. If the normal to the parabola y^2=4a x at point t1 cuts the parabola a...

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