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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 )

The axis of parabola is along the line y=x and the distance of its vertex and focus from origin are sqrt2 and 2 sqrt2 respectively. If vertex and focus both lie in the first quadrant, then find the equation of the parabola

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

If the coordinates of vertex and focus of a parabola be (2,1) & (2,3) respectively, then the axis of the parabola will be

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

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  2. Prove that for a suitable point P on the axis of the parabola y^(2)=4a...

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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 number of common chord of the parabolas x=y^(2)-6y+11andy=x^(2)-6x...

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

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

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  7. Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=...

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  8. Find the area of the greatest rectangle that can be inscribed in an ...

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  9. The auxiliary circle of a family of ellipses passes through the ori...

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  10. Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

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  11. A line passing through the origin O(0,0) intersects two concentric ...

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  12. If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2)...

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  13. Find the maximum area of an isosceles triangle inscribed in the ellips...

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  14. Find the eccentric angles of the extremities of the latus recta of ...

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  15. Find the equation of the ellipse whose axes are of length 6 and 2sq...

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  16. If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 repr...

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  17. Obtain the equation of the ellipse whose focus is the point (-1, 1), a...

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  18. The moon travels an elliptical path with Earth as one focus. The ma...

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  19. If the foci of an ellipse are (0,+-1) and the minor axis of unit lengt...

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  20. Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of ecc...

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