Find whether `x^(2)/a^(2)+y^(2)/b^(2)=1` forms a mapping or not.

Find whether f(x)=x^(3) forms a mapping or not.

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 ellipse (x^2 )/(a^2) + (y^2)/(b^2)=1 (a gt b) .

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)) .

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

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

Find the area enclosed by the circle the ellpise x^(2)/a^(2) + y^(2)/b^(2) = 1

Eccentricity of ellipse (x^(2))/(169) + (y^(2))/(25) = 1 and (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 then (a)/(b) = ……..

The differential equation satisfying the curve (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 when lambda begin arbitary uknowm, is (a) (x+yy_(1))(xy_(1)-y)=(a^(2)-b^(2))y_(1) (b) (x+yy_(1))(xy_(1)-y)=y_(1) ( c ) (x-yy_(1))(xy_(1)+y)(a^(2)-b^(2))y_(1) (d) None of these

Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and a concentric circle of radius rdot