Ellipse · Mathematics · WB JEE

If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

The equation of the ellipse having vertices at ($$\pm$$ 5, 0) and foci ($$\pm$$ 4, 0) is

The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

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...

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...

The length of the latus rectum of the ellipse is 16x2 + 25y2 = 400 is

The equation 8x2 + 12y2 $$-$$ 4x + 4y $$-$$ 1 = 0 represents

The equation $$\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta$$ represents the curve

A line of fixed length $$\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}$$ moves so that its ends are always on two fixed perpendicular straight li...

With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is

The tangent at point $$(a\cos \theta ,b\sin \theta ),0 ...

If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$, and an extremity of its minor...

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 $$...

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 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...

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...

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

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

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 =...

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...

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...

Let f be a strictly decreasing function defined on R such that $$f(x) > 0,\forall x \in R$$. Let $${{{x^2}} \over {f({a^2} + 5a + 3)}} + {{{y^2}} \ove...

Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

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...