Home
Class 12
MATHS
The ratio of the area of triangle inscri...

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.

Text Solution

Verified by Experts

The given ratio is
`(b)/(a)=(1)/(2)`
Now, `e^(2)=1-(b^(2))/(a^(2))=1-(1)/(4)=(3)/(4)or e=(sqrt(3))/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the area of the greatest rectangle that can be inscribed in an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

Find the area of the region bounded by the ellipse (x^(2) )/( a^(2)) +( y^(2))/( b^(2))=1

The point of intersection of the tangents at the point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its corresponding point Q on the auxiliary circle meet on the line (a) x=a/e (b) x=0 (c) y=0 (d) none of these

Find the maximum area of an isosceles triangle inscribed in the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with its vertex at one end of the major axis.

The eqation of auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 is _

If the area of the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 is 4pi , then find the maximum area of rectangle inscribed in the ellipse.

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

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

Find the slope of normal to the ellipse , (x^(2))/(a^(2))+(y^(2))/(b^(2))=2 at the point (a,b).