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An ellipse has eccentricity (1)/(2) and ...

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

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ARIHANT MATHS-HYPERBOLA-Exercise (Single Option Correct Type Questions)
  1. Let A=(-3, 4) and B=(2, -1) be two fixed points. A point C moves such ...

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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. Find the 15^(th) term of the following sequence whose n^(th) term is ...

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  7. An ellipse has eccentricity (1)/(2) and one focus at the point P ((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. Find the 5^(th) term of the G.P , 1/2 , 1/4 ,1/8 ....

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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 the values of m for which the line y=mx+2sqrt(5) touches the hyperb...

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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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