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A parabola y=a x^2+b x+c crosses the x-a...

A parabola `y=a x^2+b x+c` crosses the x-axis at `(alpha,0)` and `(beta,0)` both to the right of the origin. A circle also pass through these two points. The length of a tangent from the origin to the circle is `sqrt((b c)/a)` (b) `a c^2` (c) `b/a` (d) `sqrt(c/a)`

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A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0)(beta,0) both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is: (a) sqrt((b c)/a) (b) a c^2 (c) b/a (d) sqrt(c/a)

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  2. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

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  3. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0) and (beta,0) ...

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  4. From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the...

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  5. A line A B makes intercepts of lengths a and b on the coordinate axes....

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  6. Prove that the line joining the orthocentre to the centroid of a tr...

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  7. A is a point on the parabola y^2=4a x . The normal at A cuts the parab...

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  8. The equation of the line that touches the curves y=x|x| and x^2+(y-2)^...

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  9. Let PQ be a chord of the parabola y^2=4x. A circle drawn with PQ as a...

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  10. Statement 1: Through (lambda,lambda+1) , there cannot be more than one...

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  11. Each question has four choices a, b, c and d, out of which only one is...

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  12. Statement 1: The line joining the points (8,-8)a n d(1/2,2), which are...

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  13. Statement 1: In the parabola y^2=4a x , the circle drawn the taking th...

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  14. The vertices A,B, and C of a variable right triangle lie on a parabol...

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  15. Show that the common tangents to the parabola y^2=4x and the circle x^...

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  16. Consider a curve C : y^2-8x-2y-15=0 in which two tangents T1a n dT2 ar...

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  17. Statement 1: The line a x+b y+c=0 is a normal to the parabola y^2=4a x...

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  18. Statement 1: The length of focal chord of a parabola y^2=8x making on ...

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  19. Statement 1: (5x-5)^2+(5y+10)^2=(3x+4y+5)^2 is a parabola. Statement 2...

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  20. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

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