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If the three normals from any point to the parabola `y^(2)=4x` cut the line x=2 at points whose ordinates are in AP, then prove that the slopes of tangents at the co-normal points are in GP.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. In the parabola y^(2)=4ax, the tangent at P whose abscissa is equal to...

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

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  3. If the three normals from any point to the parabola y^(2)=4x cut the l...

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  4. A ray of light moving parallel to the X-axis gets reflected from a par...

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  5. A circle and a parabola y^2=4a x intersect at four points. Show that t...

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  6. A parabolic mirror is kept along y^(2)=4x and two light rays, parallel...

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  7. If incident from point (-1,2) parallel to the axis of the parabola y^2...

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  8. Find the equation of parabola having focus at (1,1) and vertex at (-3,...

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  9. Find the equation of the parabola with focus f(4,0) and directrix x=−4...

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  10. Find the value of lambda if the equation (x-1)^2+(y-2)^2=lambda(x+y+3)...

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  11. The equation of the latus rectum of a parabola is x+y=8 and the equati...

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  12. Prove that the locus of the centre of a circle, which intercepts a cho...

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  13. Find the value of lamda if the equation 9x^(2)+4y^(2)+2lamdaxy+4x-2y+3...

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  14. Find the range of values of lamda for which the point (lamda,-1) is ex...

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  15. Prove that the locus of a point, which moves so that its distance from...

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  16. LOL' and MOM' are two chord of parabola y^(2)=4ax with vertex A passin...

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  17. If (a,b) is the midpoint of a chord passing through the vertex of the ...

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  18. If two of the three feet of normal drawn from a point to the parabola ...

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  19. If three distinct normals to the parabola y^(2)-2y=4x-9 meet at point ...

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  20. Find the locus of the point of intersection of two normals to a parabo...

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