Home
Class 12
MATHS
Find the area bounded by the ellipse (x^...

Find the area bounded by the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and the ordinates `x=a e\ a n d\ x=0,` where `b^2=a^2(1-e^2)a n d\ e<1.`

Text Solution

Verified by Experts

Required area A is given by
`=>A=2` (Area of shaded region in first quadrant)
`⇒A=2∫_0^(ae) |y|dx`
`⇒A=2(b)/a ∫_0^(ae)√(a^2-x^2) dx`
`⇒A=(2b)/a​[1/2​×sqrt(a^2−x^2) ​+1/2​a^2sin^(−1)(x/a)​]^(ae)​`
`⇒A=(2b)/a​[(ae)/2 sqrt(a^2−a^2e^2) ...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise Exercise 8.1|13 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • APPLICATION OF DERIVATIVES

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|51 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.7|17 Videos

Similar Questions

Explore conceptually related problems

Find the area bounded by the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and the ordinates x = 0 and x = a e , where, b^2=a^2(1-e^2) and e < 1 .

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

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

Find the area bounded by the curve |y|+1/2 le e^(-|x|) .

Find the area bounded by the curve y=cos x ,\ x-axis and the ordinates x=0\ a n d\ x=2pidot

If the normals at P(theta) and Q(pi/2+theta) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 meet the major axis at Ga n dg, respectively, then P G^2+Qg^2= b^2(1-e^2)(2-e)^2 a^2(e^4-e^2+2) a^2(1+e^2)(2+e^2) b^2(1+e^2)(2+e^2)

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

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

Prove that the area bounded by the circle x^2+y^2=a^2 and the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is equal to the area of another ellipse having semi-axis a-b and b ,a > b .

The area bounded by y=e^(x),y=e^(-x) and x = 2 is