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MCQ (More than One Correct Answer)
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The line y = x + 5 touches
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Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
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Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ at any point. The locus of the mid-point...
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MCQ (Single Correct Answer)
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PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OP...
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AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right ...
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Let $$P(3\sec \theta ,2\tan \theta )$$ and $$Q(3\sec \phi ,2\tan \phi )$$ be two points on $${{{x^2}} \over 9} - {{{y^2}...
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The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 =...
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The locus of the centre of a variable circle which always touches two given circles externally is
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The co-ordinate of a point on the auxiliary circle of the ellipse x2 + 2y2 = 4 corresponding to the point on the ellipse...
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The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P ...
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Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of...
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Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of...
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If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over ...
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A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OP...
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The equation 8x2 + 12y2 $$-$$ 4x + 4y $$-$$ 1 = 0 represents
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The length of the latus rectum of the ellipse is 16x2 + 25y2 = 400 is
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The eccentricity of the hyperbola $$4{x^2} - 9{y^2} = 36$$ is
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For different values of $$\alpha$$, the locus of the point of intersection of the two straight lines $$\sqrt 3 x - y - 4...
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S and T are the foci of an ellipse and B is an end point of the minor axis. If STB is an equilateral triangle, the eccen...
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If the line ax + by + c = 0 is a tangent to the curve xy = 4, then
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The angle between the line joining the foci of an ellipse to one particular extremity of the minor axis is 90$$^\circ$$....
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The line y = 2t2 intersects the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ in real point if
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The total number of tangents through the point (3, 5) that can be drawn to the ellipse 3x2 + 5y2 = 32 and 25x2 + 9y2 = 4...
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