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Find the range of parameter a for which ...

Find the range of parameter `a` for which a unique circle will pass through the points of intersection of the hyperbola `x^2-y^2=a^2` and the parabola `y=x^2dot` Also, find the equation of the circle.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Two lines are drawn at right angles, one being a tangent to y^(2)=4ax ...

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  2. The area of the trapezium whose vertices lie on the parabola y^2 = 4x ...

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  3. Find the range of parameter a for which a unique circle will pass thro...

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  4. Find the radius of the largest circle, which passes through the focus ...

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  5. A tangent is drawn to the parabola y^(2)=4ax at P such that it cuts th...

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  6. Tangents are drawn to the parabola at three distinct points. Prove t...

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  7. Statement 1: The circumcircle of a triangle formed by the lines x=0,...

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  8. Statement 1: The point of intersection of the tangents at three dist...

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  9. Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa ...

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  10. Statement 1: Normal chord drawn at the point (8, 8) of the parabola ...

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  11. Statement 1: The value of alpha for which the point (alpha,alpha^2) li...

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  12. Statement 1: If there exist points on the circle x^2+y^2=a^2 from whic...

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  13. Let L be a normal to the parabola y^(2)=4x. If L passes through the po...

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  14. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

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  15. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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  16. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+c)=0 ...

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  17. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

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  18. If y+3=m1(x+2) and y+3=m2(x+2) are two tangents to the parabola y^2=8x...

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  19. A line of slope lambda(0 < lambda < 1) touches the parabola y+3x^2=0 a...

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  20. If y=2x-3 is tangent to the parabola y^(2)=4a(x-(1)/(3)), then a is eq...

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