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An ellipse has eccentricity 1/2 and one...

An ellipse has eccentricity `1/2` and one focus at the point `P(1/2,1)`. Its one directrix is the comionand tangent nearer to the point the P to the hyperbolaof `x^2-y^2=1` and the circle `x^2+y^2=1`.Find the equation of the ellipse.

A

`9x^(2)+12y^(2)=108`

B

`9(x-(1)/(3))^(2)+12(y-1)^(2)=1`

C

`9(x-(1)/(3))^(2)+4(y-1)^(2)=36`

D

None of these

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The correct Answer is:
B
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ARIHANT MATHS-HYPERBOLA-Exercise (Single Option Correct Type Questions)
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  2. A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-...

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

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  4. If alpha+beta=3pi , then the chord joining the points alpha and beta f...

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  5. If x^2/a^2+y^2/b^2=1(a>b) and x^2-y^2=c^2 cut at right angles, then:

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  6. Chords of the hyperbola, x^2-y^2 = a^2 touch the parabola, y^2 = 4ax. ...

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  7. An ellipse has eccentricity 1/2 and one focus at the point P(1/2,1)....

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  8. The equation of the line passing through the centre of a rectangular h...

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  9. The condition that a straight line with slope m will be normal to para...

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  10. Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4...

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  11. The co-ordinates of the centre of the hyperbola, x^2+3x y+3y^2+2x+3y+2...

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  12. Let F1,F2 are the foci of the hyperbola x^2/16-y^2/9=1 and F3,F4 are t...

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  13. Locus of the point of intersection of the tangents at the points with ...

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  14. Latusrectum of the conic satisfying the differential equation xdy+ydx=...

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  15. The point of intersection of the curve whose parametrix equations are ...

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  16. If the tangent and normal to a rectangular hyperbola cut off intercept...

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  17. The focus of rectangular hyperbola (x-a)*(y-b)=c^2 is

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  18. The equation of a hyperbola conjugate to the hyperbola x^(2)+3xy+2y^(2...

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  19. If values of a, for which the line y=ax+2sqrt(5) touches the hyperbola...

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  20. Let C be a curve which is the locus of the point of intersection of li...

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