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If the 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 ENGLISH-CONIC SECTIONS-All Questions
  1. In the parabola y^2=4a x , then tangent at P whose abscissa is equal t...

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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 normals from any point to the parabola y^2=4x cut the line x=2 ...

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  4. If (h,k) is a point on the axis of the parabola 2{(x-1)^2 + (y-1)^2} =...

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

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

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  7. A parabola mirror is kept along y^2=4x and two light rays parallel to ...

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

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

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

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

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

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  13. Prove that the locus of the center of a circle, which intercepts a cho...

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  14. Find the value of lambda if the equation 9x^2+4y^2+2lambdax y+4x-2y+3=...

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  15. Find the range of values of lambda for which the point (lambda,-1) is ...

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

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  17. L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A ...

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

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  19. If two of the three feet of normals drawn from a point to the parabola...

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  20. If three distinct normals can be drawn to the parabola y^2-2y=4x-9 fro...

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