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The number of points on the hyperbola (x...

The number of points on the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=3` from which mutually perpendicular tangents can be drawn to the circle `x^2+y^2=a^2` is/are 0 (b) 2 (c) 3 (d) 4

A

0

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Director circle of the circle `x^(2)+y^(2)=a^(2)" is "x^(2)+y^(2)=2a^(2)`.
The semi-transverse axis is `sqrt3a`.
The radius of the circle is `sqrt2a`.
Hence, director circle and hyperbola do not intersect.
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CENGAGE-HYPERBOLA-Exercise (Single)
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  2. If tangents P Qa n dP R are drawn from a variable point P to thehyperb...

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  3. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=3 from w...

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

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

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

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  7. The locus of the point which is such that the chord of contact of t...

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

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

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  10. Let P(a sectheta, btantheta) and Q(aseccphi , btanphi) (where theta+...

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

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

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

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

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  15. For hyperbola whose center is at (1, 2) and the asymptotes are paralle...

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  16. The asymptotes of the hyperbola (x^(2))/(a(1)^(2))-(y^(2))/(b(1)^(2))=...

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  17. If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then...

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  18. If two distinct tangents can be drawn from the Point (alpha,2) on diff...

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  19. A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x...

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  20. From any point to the hyperbola ^2/a^2-y^2/b^2=1, tangents are drawn ...

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