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If `P S Q` is a focal chord of the parabola `y^2=8x` such that `S P=6` , then the length of `S Q` is 6 (b) 4 (c) 3 (d) none of these

A

6

B

4

C

3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Since the semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola, SP, 4,SQ are in H.P. Therefore,
`4=(2SPxxSQ)/(SP+SQ)`
`or4=(2(6)(SQ))/(6+SQ)`
`or24+4(SQ)=12(SQ)`
`orSQ=3`
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CENGAGE-PARABOLA-Exercise (Single)
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  2. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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

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  20. If the locus of the middle of point of contact of tangent drawn to the...

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