The area between `x^2/a^2+y^2/b^2=1` and the straight line `x/a+y/b=1` is
(A) `1/2piab`
(B) `1/2ab`
(C) `(piab)/4-(ab)/2`
(D) `1/4ab`

Area of the ellipse x^2/a^2+y^2/b^2=1 is piab

Prove that the ellipse x^2/a^2 + y^2/b^2 = 1 and the circle x^2 + y^2 = ab intersect at an angle tan^(-1) (|a-b|/sqrt(ab)) .

Area of the quadrilateral formed with the foci of the hyperbola x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1 (a) 4(a^2+b^2) (b) 2(a^2+b^2) (c) (a^2+b^2) (d) 1/2(a^2+b^2)

Show that the tangent of an angle between the lines x/a+y/b=1 and x/a-y/b=1\ i s(2a b)/(a^2-b^2)

If a=1+b+b^2+b^3+…..to oo where |b|lt1 then roots of equation ax^2+x-ab=0 are (A) -1,ab (B) 1,b (C) -1, b (D) -1,a

The area of the triangle formed by the lines y=a x ,x+y-a=0 and the y-axis is (a) 1/(2|1+a|) (b) 1/(|1+a|) (c) 1/2|a/(1+a)| (d) (a^2)/(2|1+a|)

Show that the length of the chord intercepted by the ellipse x^2/a^2 + y^2/b^2 = 1 on the line y= mx + c is 2ab/(a^2 m^2 + b^2) sqrt((1+m^2) (a^2 m^2 + b^2 - c^2))

If the family of curves y=ax^2+b cuts the family of curves x^2+2y^2-y=a orthogonally, then the value of b = (A) 1 (B) 2/3 (C) 1/8 (D) 1/4

Show that the tangent of an angle between the lines (x)/(a)+(y)/(b)=1 and (x)/(a)-(y)/(b)=1 and (2ab)/(a^(2)-b^(2)) .

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2