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A circle and a parabola y^2=4a x interse...

A circle and a parabola `y^2=4a x` intersect at four points. Show that the algebraic sum of the ordinates of the four points is zero. Also show that the line joining one pair of these four points is equally inclined to the axis.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If (h,k) is a point on the axis of the parabola 2{(x-1)^2 + (y-1)^2} =...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the locus of thepoint of intersection of two normals to a parabol...

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  19. P(t1) and Q(t2) are the point t1a n dt2 on the parabola y^2=4a x . The...

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  20. Prove that the locus of the point of intersection of the normals at th...

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