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`

Angle between the curve x^2/a^2+y^2/b^2=1 and x^2+y^2=ab,a gt b .

Area bounded by the parabola y^2=x and the line 2y=x is (A) 4/3 (B) 1 (C) 2/3 (D) 1/3

The area enclosed in the region (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is (i) (pi ab)/(4)-(1)/(2)ab( ii (pi ab)/(4) (iii) piab (iv) none of these

Area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is pi ab

If log_(2)7= a and log_(3)2=b ," then the value of log_(14)84 is : (A) (1+3b+2ab)/(ab-b) (B) (1+2b+ab)/(b+ab) (C) (1+a+b)/(a+b) (D) (1+b+ab)/(a+ab)

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

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

The value of the integral int_0^(pi/4) dx/(a^2cos^2x+b^2sin^2x)= (A) 1/(ab)tan^-1(b/a)(a,bgt0) (B) 1/(ab)tan^-1(b/a)(a,blt0) (C) pi/4(a=1,b=1) (D) none of these

The intercept on the line y=x by the circle x^2+y^2-2x=0 is AB. Equation of the circle with AB as a diameter is (A) (x-1/2)^3+(y-1/2)^2=1/2 (B) (x-1/2)^2+(y-1/2)^2=1/4 (C) (x+1/2)^2+(y+1/2)^2=1/2 (D) (x+1/2)^2+(y+1/2)^2=1/4