Home
Class 12
MATHS
An ellipse passes through the point (2,3...

An ellipse passes through the point (2,3) and its axes along the coordinate axes, `3x +2y -1 = 0` is a tangent to the ellipse, then the equation of the ellipse is

A

`(x^(2))/(4)+4y^(2) =1`

B

`(x^(2))/(8)+(y^(2))/(1)=1`

C

`4x^(2) +(y^(2))/(4) =1`

D

No such ellipse exists

Text Solution

Verified by Experts

The correct Answer is:
D

From the position of line and point, it is clear that no such ellipse exists.
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

  • EQAUTION OF STRAIGHT LINE AND ITS APPLICATION

    CENGAGE PUBLICATION|Exercise DPP 3.2|13 Videos

Similar Questions

Explore conceptually related problems

An ellipse passes through the point (4,-1) and touches the line x+4y-10=0 . Find its equation if its axes coincide with the coordinate axes.

An ellipse is drawn by taking a diameter of the circle (x-1)^(2) + y^(2) = 1 as its semi-minor axis and a diameter of the the circle x^(2) +(y - 2)^(2) = 4 as its sem-major axis . If the centre of the ellipse is at the origin and its axes are the coordinate axes , then the equation of the ellipse is _

The eccentricity of an ellipse is (1)/(sqrt(3)) , the coordinates of focus is (-2,1) and the point of intersection of the major axis and the directrix is (-2,3) . Find the coordinates of the centre of the ellipse and also equation of the ellipse .

An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (pmsqrt2,0) (d) equation of ellipse is x^2+ 2y^2 =1

An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (+-sqrt 2, 0) (d) equation of ellipse is (x^2 +y^2 =4)

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 eccentricity of an ellipse is (2)/(3) and the coordinates of its focus and the corresponding vertex are (1,2) and (2,2) respectively. Find the equation of the ellipse . Also find the coordinate of the point of intersection of its major axis and the directrix in the same direction .

If a circle passes through the points of intersection of the coordinates axes with the lines lambdax-y+1=0 and x-2y+3=0 , then find the value of lambda .

The eccentricity of an ellipse is (4)/(5) and the coordinates of its one focus and the corresponding vertex are (8,2) and (9,2) . Find the equation of the ellipse. Also find in the same direction the coordinates of the point of intersection of its major axis and the directrix.

The lengths of major and minor axes of an ellipse are 8 and 6 and their equations are y - 1 = 0 and x + 3 = 0 respectively . Find the equation of the ellipse .