Home
Class 12
MATHS
An ellipse is inscribed in a reactangle ...

An ellipse is inscribed in a reactangle and the angle between the diagonals of the reactangle is `tan^(-1)(2sqrt(2))`, then find the ecentricity of the ellipse

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(sqrt(2))`

From the figure, we have
`tan.(theta)/(2)=(b)/(a)rArrtan^(2).(theta)/(2)=(b^(2))/(a^(2))`
`rArr(1-costheta)/(1+cos theta)=(b^(2))/(a^(2))`
`rArr(1-(1)/(3))/(1+(1)/(3))=(b^(2))/(a^(2))rArr(b^(2))/(a^(2))=(1)/(2)`
`:. e=sqrt(1-(b^(2))/a^(2))=(1)/(sqrt(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the distance between the foci of the ellipse 3x^(2) + 4y^(2) = 12 .

The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse. (A) 1/2 (B) sqrt3/2 (C) 1/sqrt2 (D) 1/sqrt3

If the angle between the lines joining the end points of minor axis of an elipes with its one focus is pi/2, then the eccentricity of the ellipse is-

If the normal at one end of lotus rectum of an ellipse passes through one end of minor axis then prove that, e^(2)=(sqrt(5)-1)/(2) , where e is the eccentricity of the ellipse.

An ellipse has OB as a semi-minor axis, F and F' are its two foci and the angle FBF' is a right angle. Find the eccentricity of the ellipse.

In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is sqrt(10) - sqrt(5) . The equation of the ellipse (a) (x^(2))/(36) +(y^(2))/(18) = 1 (b) (x^(2))/(40)+(y^(2))/(20) = 1 (c) (x^(2))/(20) +(y^(2))/(10) = 1 (d) (x^(2))/(10)+(y^(2))/(5) =1

The angle between the pair of tangents drawn to the ellipse 3x^(2) + 2y^(2) =5 from the point (1, 2) is-

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

Find the angle between the pair of tangents from the point (1,2) to the ellipse 3x^2+2y^2=5.

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