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The number of common chords of the parab...

The number of common chords of the parabolas `x=y^2-6y+11` and `y=x^2-6x+11` is 1 (b) 2 (c) 4 (d) 6

A

1

B

2

C

4

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
(4) We have parabolas `x-2=(y-3)^(2)andy-2=(x-3)^(2)`
Parabolas are symmetrical about line y=x.

These parabola intersect at four points.
So, number of chords `=.^(4)C_(2)=6`
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CENGAGE-PARABOLA-Exercise (Single)
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  2. A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0)(beta,0) both ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. The straight lines joining any point P on the parabola y^2=4a x to the...

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