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An ellipse intersects the hyperbola 2x^2...

An ellipse intersects the hyperbola `2x^2- 2y^2 = 1` orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the co-ordinate axes, then :

A

Equation of ellipse is`x^2 2y^2 = 2`

B

The foci of ellipse are `(+- 1, 0)`

C

Equation of ellipse is `x^2 2y^2 =4`

D

The foci of ellipse are `(+- 2, 0)`.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. The normal at a point P, on the ellipse x^2+4y^2=16 meets the x-axis a...

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  2. The locus of the orthocentre of the triangle formed by the lines : (1 ...

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  3. An ellipse intersects the hyperbola 2x^2- 2y^2 = 1 orthogonally. The e...

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  4. The lines p(p^(2)+1)x-y+q=0 and (p^(2)+1)^(2)x+(p^(2)+1)y+2q = 0 are ...

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  5. If P and Q are the points of intersection of the circles x^(2)+y^(2)+3...

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  6. The ellipse x^2+ 4y^2 = 4 is inscribed is a rectangle alligned with th...

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  7. The Line L given by (x)/(5) + (y)/(b) =1 passes through the point (13,...

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  8. The circle x^(2)+y^(2d)=4x+8y+5 intersects the line 3x-4y=m at two dis...

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  9. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

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  10. Let A and B be two distinct points on the parabola y^2=4x. If the axis...

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  11. A straight line L through the point (3,-2) is incined at an angle 60^...

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  12. The lines x + y =|a| and ax-y= 1 intersect each other in the first qua...

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  13. If A (2, -3) and B (-2, 1) are two vertices of a triangle and third ve...

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  14. The two circles x^2+""y^2=""a x and x^2+""y^2=""c^2(c"">""0) touch eac...

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  15. The circle passing through the point (-1,0) and touching the Y-axis at...

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  16. Find the equation of the circle passing through (1,0) and (0,1) and h...

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  17. Let (x,y) be any point on the parabola y^2= 4x . Let P be the point th...

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  18. Find the equation of the ellipse referred to its axes as the axes of c...

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  19. The equation of the hyperbola whose foci are (- 2, 0) and (2, 0) and e...

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  20. Find the equation of the diagonal through the origin of the quadrilate...

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