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Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola `16y^2 -9 x^2 = 1` is

A

`x^(2)+y^(2)=9`

B

`x^(2)+y^(2)=1//9`

C

`x^(2)+y^(2)=7//144`

D

`x^(2)+y^(2)=1//16`

Text Solution

Verified by Experts

The correct Answer is:
D
`(y^(2))/(1//16)-(x^(2))/(1//9)=1`
Locus will be the auxiliary circle
`x^(2)+y^(2)=(1)/(16)`
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CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
  1. The number of possible tangents which can be drawn to the curve 4x^2-9...

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  2. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

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  3. Locus of the feet of the perpendiculars drawn from either foci on a va...

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  4. P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, and N...

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  5. The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 wh...

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  6. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 me...

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  7. The locus of a point, from where the tangents to the rectangular hyp...

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  8. If tangents P Qa n dP R are drawn from a variable point P to thehyperb...

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  9. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 from w...

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  10. If a ray of light incident along the line 3x+(5-4sqrt(2))y=15 gets ref...

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  11. The chord of contact of a point P w.r.t a hyperbola and its auxiliary ...

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  12. The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at r...

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  13. The locus of the point which is such that the chord of contact of ta...

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  14. If x=9 is the chord of contact of the hyperbola x^2-y^2=9 then the equ...

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  15. If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2...

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  16. Let P(a sectheta, btantheta) and Q(asecphi , btanphi) (where theta+p...

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  17. A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on th...

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  18. Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre ...

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  19. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

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  20. Let any double ordinate P N P ' of the hyperbola (x^2)/(25)-(y^2)/(16)...

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