The equation of the tangent at the point `((ab^(2))/(a^(2)+b^(2)),(a^(2)b)/(a^(2)+b^(2)))` of the circle `x^(2)+y^(2)=(a^(2)b^(2))/(a^(2)+b^(2))` is

Find the equation of the tangent at the point (x,y) of the curve : (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

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

Find the equation of the tangent to the curve (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (sqrt(2)a, b) .

Slope of the common tangent to the ellipse (x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1,(x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1 is

Prove that matrix [((b^(2)-a^(2))/(a^(2)+b^(2)),(-2ab)/(a^(2)+b^(2))),((-2ab)/(a^(2)+b^(2)),(a^(2)-b^(2))/(a^(2)+b^(2)))] is orthogonal.

If chord of contact of the tangent drawn from the point (a,b) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=k^(2), then find the locus of the point (a,b).

(a)/(x)-(b)/(y)=0,(ab^(2))/(x)+(a^(2)b)/(y)=a^(2)+b^(2)

The locus of the middle points of the portions of the tangents of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 included between the axis is the curve (a) (x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(4) (b) quad (a^(2))/(x^(2))+(b^(2))/(y^(2))=4 (c) a^(2)x^(2)+b^(2)y^(2)=4 (d) b^(2)x^(2)+a^(2)y^(2)=4

which one of the following is the common tangent to the ellipses,(x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1?