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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)(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: `sqrt((b c)/a)` (b) `a c^2` (d) `sqrt(c/a)`

A

`sqrt(bc//a)`

B

`ac^(2)`

C

b/a

D

`sqrt(c//a)`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) `OT^(2)=OA*OB=alphabeta=(c)/(a)`
`orOT=sqrt((c)/(a))`
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CENGAGE-PARABOLA-Exercise (Single)
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  4. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

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  5. Two parabola have the same focus. If their directrices are the x-axis ...

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  6. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

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

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  8. The triangle PQR of area 'A' is inscribed in the parabola y^2=4ax such...

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  9. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

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  10. If aa n dc are the lengths of segments of any focal chord of the parab...

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  11. If x=m x+c touches the parabola y^2=4a(x+a), then c=a/m (b) c=a m+a/...

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  12. The area of the triangle formed by the tangent and the normal to the ...

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  13. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) where c1 and c2 are variables, ...

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

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

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  16. The locus of the center of a circle which cuts orthogonally the parabo...

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  17. If the parabola y=a x^2-6x+b passes through (0,2) and has its tangent ...

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  18. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

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  19. The tangent to y^(2)=ax make angles theta(1)andtheta(2) with the x-axi...

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

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