Home
Class 12
MATHS
What is the eccentricity of the ellipse ...

What is the eccentricity of the ellipse `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 ` if length of its minor axis is equal to the distance between its foci ?

Text Solution

Verified by Experts

The correct Answer is:
`e = (1)/(sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBHS Archive (2015)|10 Videos
  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBHS Archive (2016)|11 Videos
  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBHS Archive (2013)|15 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion - Reason Type)|2 Videos
  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION ( ASSERTION-REASON TYPE )|2 Videos

Similar Questions

Explore conceptually related problems

If e be the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 , then e =

Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose latus reactum is half of its major axis.

What is the eccentricity of the ellipse whose length of minor axis is equal to the distance between the two foci?

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

Find the eccentricity of the ellipse if the length of minor axis is equal to half the distance between the foci of the ellipse .

Consider an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b) . A hyperbola has its vertices at the extremities of minor axis of the ellipse and the length of major axis of the ellipse is equal to the distance between the foci of hyperbola. Let e_(1) and e_(2) be the eccentricities of ellipse and hyperbola, respectively. Also, let A_(1) be the area of the quadrilateral fored by joining all the foci and A_(2) be the area of the quadrilateral formed by all the directries. The relation between e_(1) and e_(2) is given by

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci , is

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is : (1) 4/3 (2) 4/(sqrt(3)) (3) 2/(sqrt(3)) (4) sqrt(3)

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.