Parabola

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Consider a point P on a parabola such that 2 of the normal drawn from it to the parabola are at right angles on parabola, then If P -= (x _(1), y _(1)), the slope of third normal is, if If the equation of parabola is y^(2)= 8x

Consider a point P on a parabola such that 2 of the normal drawn from it to the parabola are at night angles on parabola, then The ratio of latus rectum of given parabola and that of made by locus of point P is

The endpoints of two normal chords of a parabola are concyclic.Then the tangents at the feet of the normals will intersect (a) at tangent at vertex of the parabola (b) axis of the parabola (c) directrix of the parabola (d) none of these

Consider two parabola y=x^(2)-x+1 and y=x^(2)+x+(1)/(2), the parabola y=-x^(2)+x+(1)/(2) is fixed and parabola y=-x^(2)+1 rolls without slipping around the fixed parabola,then the locus of the focus of the moving parabola is

MODERN PUBLICATION-CONIC SECTIONS -OBJECTIVE TYPE QUESTIONS (VERY SHORT ANSWER TYPE QUESTIONS)
  1. Parabola

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  2. Ellipse

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  3. Hyperbola

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  4. Define eccentricity of an ellipse

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  5. Determine whether the following represents a circle , a point or no ci...

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  6. Find the equation of circle whose centre is (1/2, 1/2) and radius is 1...

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  7. Find the parametric equation of the circles : x^2 + y^2 + 2x - 4y - 1 ...

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  8. Show that the point (x, y), where x=a+r cos theta, y = b + r sin theta...

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  9. Find the equation of the circle when the end points of a diameter of t...

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  10. The equation of the parabola with vertex at the origin passing through...

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  11. Find the equation of the parabola with focus at (3, -4) and directrix ...

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  12. Find the lengths of major and minor axes of the ellipse : (x^(2))/(4...

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  13. Find the lengths of the major and the minor axes, the coordinates of t...

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  14. Find the length of the latus -rectum of the ellipse : (x^(2))/(4) + ...

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  15. The equation of the ellipse whose centre is at origin and which passes...

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  16. Find the equation of the ellipse in the following case: eccentricity e...

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  17. Find the eccentricity of an ellipse if its latus rectum is equal to on...

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  18. The eccentricity of the ellipse if the distance between the foc...

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  19. Find the equation of the ellipse whose major axis is 8 and eccentricit...

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  20. Find the equation of the hyperbola having : vertices (0, +-3) and foci...

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