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A double ordinate of the parabola y^2=4a...

A double ordinate of the parabola `y^2=4ax` is of length 8a. Prove that the lines from the Vertex to its two ends are at right angles.

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The directrix of the parabola y^2=4ax is :

The focus of the parabola y^2= 4ax is :

The vertex of the parabola y^2=4a(x+a) is:

PQ is a double ordinate of a parabola y^2=4a xdot Find the locus of its points of trisection.

The angle between a pair of tangents drawn from a point P to the parabola y^2= 4ax is 45^@ . Show that the locus of the point P is a hyperbola.

The area cut off by the parabola y^2 = 4ax , (a gt 0) and its latus rectum is

If a tangent to the parabola y^2 = 4ax meets the axis of the parabola in T and the tangent at the vertex A in Y, and the rectangle TAYG is completed, show that the locus of G is y^2 + ax = 0.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Find the equation of the circle, which passes through the origin and c...

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  2. Prove that the equation y^2+ 2Ax + 2By +c =0 represents a parabola who...

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  3. A double ordinate of the parabola y^2=4ax is of length 8a. Prove that ...

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  4. Prove that the equation of the parabola whose vertex and focus are on ...

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  5. Find the focus of the parabola x^2=4y

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  6. Show that the locus of the middle points of normal chords of the parab...

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  7. If any tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cuts off inter...

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  8. The vertices of a quadrilateral are situated at foci and the extremiti...

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  9. Find the equation of the hyperbola whose foci are (8, 3), (0, 3) and w...

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  10. Find the slope of the line passing through the points : (3, - 2) and...

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  11. The slope of the line passing through the points (3,-2) and (-1,4) is:

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  12. Slope of the line passing through the points (3, -2) and (3, 4) is:

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  13. If the equation of a circle is: x^2 + y^2 + 8x -10y+8=0, then its cent...

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  14. The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

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  15. If the equation of a circle is: x^2 + y^2-4x-8y -45 =0, then its centr...

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  16. The centre of the circle x^2+y^2+8x+10y-8=0 is:

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  17. The radius of the circle : x^2 + y^2-8x + 10y- 12 =0 is:

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  18. The directrix of the parabola y^2=4ax is :

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  19. The directrix of the parabola y^(2) + 4x + 3 = 0 is :

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  20. The focus of the parabola y^2= 4ax is :

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