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If a line `y=3x+1` cuts the parabola `x^2-4x-4y+20=0` at `Aa n dB ,` then the tangent of the angle subtended by line segment `A B` at the origin is `(8sqrt(3))/(205)` (b) `(8sqrt(3))/(209)` `(8sqrt(3))/(215)` (d) none of these

A

`8sqrt(3)//205`

B

`8sqrt(3)//209`

C

`8sqrt(3)//215`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2) The joint equation of OA and OB is
`x^(2)-4x(y-3x)-4y(y-3x)+20(y-3x)^(2)=0`
(Making the equation of the parabola homogeneous using straight line)
`or193x^(2)+16y^(2)-112xy=0`
`tantheta=(2sqrt(h^(2)-ab))/(a+b)`
`=(2sqrt(56^(2)-193xx16))/(193+16)`
`=(8sqrt(3))/(209)`
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CENGAGE-PARABOLA-Exercise (Single)
  1. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

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  2. The length of the chord of the parabola y^2=x which is bisected at the...

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  3. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at Aa n dB , then th...

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  4. If P is a point on the parabola y^2=3(2x-3) and M is the foot perpendi...

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

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  6. The number of common chords of the parabolas x=y^2-6y+11 and y=x^2-6x+...

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  7. Two parabolas have the same focus. If their directrices are the x- and...

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

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

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  10. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

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

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

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

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  15. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) , where c1a n dc2 are variable,...

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

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

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

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

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

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