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Show that the equation 9`x^2-16 y^2-18 x+32 y-151=0` represents a hyperbola. Find the coordinates of the centre, lengths of the axes, eccentricity, latus-rectum, coordinates of foci and vertices, equations of the directrices of the hyperbola.

A

The length of the transverse axes is 4

B

Length of latus rectum is 9

C

Equation of directrix is `x=(21)/(5)` and `x=(11)/(5)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-HYPERBOLA-EXERCISE-2 (Level-I)
  1. Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperb...

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  2. The length of the transverse axis of a hyperbola is 7 and it passes th...

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  3. lf the eccentricity of the hyperbola x^2-y^2(sec)alpha=5 is sqrt3 ti...

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  4. If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola ...

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  5. If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1...

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  6. The equation of the chord joining two points (x(1),y(1)) and (x(2),y(2...

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  7. The locus of the foot of the perpendicular from the centre of the hype...

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  8. Find the equations to the common tangents to the two hyperbolas (x^2)/...

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

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  10. Area of triangle formed by tangent to the hyperbola xy = 16 at (16, 1)...

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  11. The tangent to the hyperbola xy=c^2 at the point P intersects the x-ax...

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  12. The locus of the mid points of the chords passing through a fixed poin...

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  13. From the points on the circle x^(2)+y^(2)=a^(2), tangents are drawn to...

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  14. Variable circles are drawn touching two fixed circles externally then ...

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  15. The asymptote of the hyperbola x^2/a^2+y^2/b^2=1 form with ans tangen ...

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  16. From any point on the hyperbola H(1):(x^2//a^2)-(y^2//b^2)=1 tangents ...

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  17. The tangent at P on the hyperbola x^2/a^2-y^2/b^2=1 meets the asymptot...

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