WB JEE
Mathematics
Ellipse and Hyperbola
Previous Years Questions

The total number of tangents through the point (3, 5) that can be drawn to the ellipse 3x2 + 5y2 = 32 and 25x2 + 9y2 = 450 is...
The line y = 2t2 intersects the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ in real point if
The angle between the line joining the foci of an ellipse to one particular extremity of the minor axis is 90$$^\circ$$. The eccentricity of the ellip...
If the line ax + by + c = 0 is a tangent to the curve xy = 4, then
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 eccentricity of the ellipse is...
For different values of $$\alpha$$, the locus of the point of intersection of the two straight lines $$\sqrt 3 x - y - 4\sqrt 3 \alpha = 0$$ and $$\s... The eccentricity of the hyperbola$$4{x^2} - 9{y^2} = 36$$is The length of the latus rectum of the ellipse is 16x2 + 25y2 = 400 is The equation 8x2 + 12y2$$-$$4x + 4y$$-$$1 = 0 represents Let$$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}} \over 4} = 1$$such that$$\...
AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right angle at the origin O, then $$... PQ is a double ordinate of the hyperbola$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$such that$$\Delta OPQ$$is an equilateral triangle... The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is The co-ordinate of a point on the auxiliary circle of the ellipse x2 + 2y2 = 4 corresponding to the point on the ellipse whose eccentric angle is 60$$...
The locus of the centre of a variable circle which always touches two given circles externally is
The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 = 0$$ lie on a circle. The cent...
A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OPQ$$ is equilateral, O being th...
If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over 9} = 1$$, then the area of the...
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of the curve intercepted between...
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of the curve intercepted between...
Let P(4, 3) be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at P intersects the X-axis at (16, 0)...
For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the following remains fixed when $$\al... S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentricity of the ellipse is The equation of the directrices of the hyperbola$$3{x^2} - 3{y^2} - 18x + 12y + 2 = 0$$is P is the extremity of the latusrectum of ellipse$$3{x^2} + 4{y^2} = 48$$in the first quadrant. The eccentric angle of P is The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is A point is in motion along a hyperbola$$y = {{10} \over x}$$so that its abscissa x increases uniformly at a rate of 1 unit per second. Then, the rat... Let the eccentricity of the hyperbola$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$be reciprocal to that of the ellipse x2 + 9y2 = 9, the... Let P be a point on the ellipse$${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$and the line through P parallel to the Y-axis meets the circle x2 + y2 =... Let P be the foot of the perpendicular from focus S of hyperbola$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$on the line bx$$-$$ay = 0... B is an extremity of the minor axis of an ellipse whose foci are S and S'. If$$\angle SBS'$$is a right angle, then the eccentricity of the ellipse i... The line segment joining the foci of the hyperbola$${x^2} - {y^2} + 1 = 0$$is one of the diameters of a circle. The equation of the circle is Let A($$-$$1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that$$\angle MBA$$= 2$$\angle MAB$$. Then, the point M moves... Tangents are drawn to the ellipse$${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$at the ends of both latusrectum. The area of the quadrilateral, so fo... ## MCQ (More than One Correct Answer) Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on The line y = x + 5 touches Consider a tangent to the ellipse$${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$at any point. The locus of the mid-point of the portion intercepted be... Equation of a tangent to the hyperbola 5x2$$-$$y2 = 5 and which passes through an external point (2, 8) is A hyperbola, having the transverse axis of length 2sin$$\theta is confocal wit6h the ellipse 3x2 + 4y2 = 12. Its equation is
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