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If the normals to the parabola `y^2=4a x` at three points `(a p^2,2a p)` and `(a q^2,2a q)` and `(a r^2,2ar)` are concurrent, then the common root of equations `P x^2+q x+r=0` and `a(b-c)x^2+b(c-a)x+c(a-b)=0` is (a) `p` (b) `q` (c) `r` (d) `1`

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If the normals to the parabola y^2=4a x at three points (a p^2,2a p), and (a q^2,2a q) are concurrent, then the common root of equations P x^2+q x+r=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 is p (b) q (c) r (d) 1

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The value of p and q(p!=0,q!=0) for which p ,q are the roots of the equation x^2+p x+q=0 are (a) p=1,q=-2 (b) p=-1,q=-2 (c) p=-1,q=2 (d) p=1,q=2

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If a, b, c are rational and the tangent to the parabola y^2 = 4kx , at P(p, q) and Q(q, b) meet at R(r, c) , then the equation ax^2 + bx-2c=0 has (A) imaginary roots (B) real and equal roots (C) rational roots (D) irrational roots

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Match the following. Normals are drawn at points P Q and R lying on th...

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  2. Tangents and normal drawn to the parabola y^2=4a x at point P(a t^2,2a...

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  3. If the normals to the parabola y^2=4a x at three points (a p^2,2a p) a...

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  4. Normal AO,AA(1),andAA(2) are drawn to the parabola y^(2)=8x from the p...

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  5. If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is ...

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  6. The length of the latus rectum of the parabola whose focus is ((u^2)/(...

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  7. If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal...

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  8. The normal at the point P(ap^2, 2ap) meets the parabola y^2= 4ax again...

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  9. The set of points on the axis of the parabola y^2=4x+8 from which the ...

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  10. Which one of the following equation represent parametric equation to a...

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  11. The vertex of a parabola is the point (a , b) and the latus rectum is ...

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  12. The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q...

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  13. Prove that the equation of the parabola whose focus is (0, 0) and tang...

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  14. A parabola is drawn touching the axis of x at the origin and having it...

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  15. The equation of the parabola whose vertex and focus lie on the axis of...

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  16. Prove that for a suitable point P on the axis of the parabola, chord A...

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  17. Two parabolas have the same focus. If their directrices are the x- and...

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  18. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

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  19. Find the equation of the curve whose parametric equations are x=1+4c...

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  20. Prove that any point on the ellipse whose foci are (-1,0) and (7,0)...

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