Home
Class 12
MATHS
The straight line bx+ay=ab divides the e...

The straight line `bx+ay=ab` divides the ellipse `b^(2)x^(2) +a^(2)y^(2) =a^(2)b^(2)` into two parts. Prove that the area of the smaller part is `(ab)/(4) (pi-2)` square units.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MODEL TEST PAPER-11

    ICSE|Exercise SECTION-C|9 Videos

  • MODEL TEST PAPER-11

    ICSE|Exercise SECTION-C|9 Videos

  • MODEL TEST PAPER 20

    ICSE|Exercise SECTION C |10 Videos

  • MODEL TEST PAPER-12

    ICSE|Exercise SECTION-C |10 Videos

Similar Questions

Explore conceptually related problems

The area bounded by the ellipse b^(2)x^(2) + a^(2) y^(2) = a^(2) b^(2) is

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

Divide : 18a^(3)b^(2) - 27 a^(2)b^(3) +9ab^(2) by 3ab

Does the straight line (x)/(a)+(y)/(b)=2 touch the ellipse (x/a)^(2)+(y/b)^(2)=2? justify.

The area enclosed by the circle x^2+(y+2)^2=16 is divided into two parts by the x-axis. Find by integration, the area of the smaller part.

The circle x^(2)+y^(2) =4a^(2) is divided into two parts by the line x =(3a)/(2). Find the ratio of areas of these two parts.

The circle x^(2) + y^(2)=8 is divided into two parts by the parabola 2y=x^(2) . Find the area of both the parts.

If straight line lx + my + n=0 is a tangent of the ellipse x^2/a^2+y^2/b^2 = 1, then prove that a^2 l^2+ b^2 m^2 = n^2.

If area of the ellipse (x^(2))/(16)+(y^(2))/(b^(2))=1 inscribed in a square of side length 5sqrt(2) is A, then (A)/(pi) equals to :

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