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Two parabola have the same focus. If the...

Two parabola have the same focus. If their directrices are the x-and the y-axis, respectively, then the slope of their common chord is

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Two parabola have the same focus. If their directrices are the x-axis and the y-axis respectively, then the slope of their common chord is :

Let A and B be two distinct points on the parabola y^2=4x . If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

The line x+ y +2=0 is a tangent to a parabola at point A, intersect the directrix at B and tangent at vertex at C respectively. The focus of parabola is S(a, 0) . Then

show that the equation of the parabola whose vertex and focus are on the x -axis at distances a and a' from the origin respectively is y^(2) = 4 (a'-a) (x - a )

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Let A, B be two distinct points on the parabola y^(2)=4x . If the axis of the parabola touches a circle of radius r having AB as diameter, the slope of the line AB is

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

The distance of two points P and Q on the parabola y^(2) = 4ax from the focus S are 3 and 12 respectively. The distance of the point of intersection of the tangents at P and Q from the focus S is

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The equation of the directrix of the parabola with vertex at the origin and having the axis along the x-axis and a common tangent of slope 2 with the circle x^2+y^2=5 is (are) x=10 (b) x=20 x=-10 (d) x=-20

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

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  2. y=x+2 is any tangent to the parabola y^(2)=8x. The point P on this tan...

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  3. Two parabola have the same focus. If their directrices are the x-and t...

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  4. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

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  5. The length of the chord of the parabola y^(2)=x which is bisected at t...

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  6. The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the l...

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  7. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

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  8. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

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  9. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

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  10. Let S be the focus of y^2=4x and a point P be moving on the curve s...

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  11. If a!=0 and the line 2b x+3c y+4d=0 passes through the points of ...

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  12. If y(1),y(2),andy(3) are the ordinates of the vertices of a triangle i...

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  13. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

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  14. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

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  15. Parabolas y^(2)=4a(x-c(1))andx^(2)=4a(y-c(2)), where c(1) and c(2) are...

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  16. A circle touches the x-axis and also touches the circle with centre (0...

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  17. The locus of the vertex of the family of parabolas y=(a^(3)x^(2))/(3...

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  18. Let C(1)andC(2) be, respectively, the parabola x^(2)=y-1andy^(2)=x-1. ...

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  19. If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then ...

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  20. The locus of a point on the variable parabola y^2=4a x , whose distanc...

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