Find the equation of the common tangent in the first quadrant of the circle `x^2+y^2=16` and the ellipse `x^2/25+y^2/4=1`.Also find the length of the intercept of the tangent between the coordinates axes.

Find the equations of the common tangents to the circle x^(2)+y^(2)=8 and the parabola y^(2)=16x

Find the equation of the common tangent of y^(2)=4ax and x^(2)=4ay.

Equation of a common tangent to the circle x^2+y^2=16 , parabola x^2=y-4 and the ellipse x^2/25+y^2/16=0 is

The equation of a common tangent to the parabola y=2x and the circle x^(2)+y^(2)+4x=0 is

Find the equation of the common tangent to the circle x^2 + y^2 = 16 and the ellipse 4x^2 + 25y^2 = 100 cutting off positive intercepts on the axes of reference. Also, find the intercept on the common tangent between the coordinate axes.

Find the area enclosed between first quadrant of a circle x^(2)+y^(2)=16 and line y=x

If tangents are drawn to the ellipse 2x^(2) + 3y^(2) =6 , then the locus of the mid-point of the intercept made by the tangents between the co-ordinate axes is