Home
Class 12
MATHS
The eccentricity of an ellipse is (1)/(...

The eccentricity of an ellipse is `(1)/(2) ` and its one focus is at S(3,2) , if the vertex nearer of S be A (5,4) , find the equation of the ellipse .

Text Solution

Verified by Experts

The correct Answer is:
`8[(x-3)^(2) + (y-2)^(2)] = (x + y - 17)^(2) ` , which is the required equation of the ellipse .
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise M . C . Q|20 Videos

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Very Short Answer Type Qustions|33 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

  • GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type-|2 Videos

Similar Questions

Explore conceptually related problems

The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

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 eccentricity of the ellipse 25 x^(2) + 4y^(2) = 100 is _

The eccentricity of the ellipse 4x^(2) + 25y^(2) = 100 is _

The eccentricity of an ellipse is (2)/(3) focus is S(5,4) and the major axis and directrix intersect at Z(8,7) . Find the coordinates of the centre of the ellipse .

The eccentricity of an ellipse is (1)/(2) , focus is S (0,0) and the major axis and directrix intersect at Z (-1,-1) . Find the coordinates of the centre of the ellipse .

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 .

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 .

The vertices of an ellipse ar (-1,2) and (9,2) . If the distance between its foci be 8 , find the equation of the ellipse and the eqations of its directrice .

The coordinates of the focus of an ellipse are (1,2) and eccentricity is (1)/(2) , the equation of its directrix is 3x + 4y - 5 = 0 . Find the equation of the ellipse.