A tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` cuts the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at `Pa n dQ` . Show that the locus of the midpoint of `P Q` is `((x^2)/(a^2)+(y^2)/(b^2))^2=(x^2)/(a^2)-(y^2)/(b^2)dot`

A tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at P and Q. Show that the locus of the midpoint of PQ is ((x^(2))/(a^(2))+(y^(2))/(b^(2)))^(2)=(x^(2))/(a^(2))-(y^(2))/(b^(2))

Length of common tangents to the hyperbolas (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(a^(2))-(x^(2))/(b^(2))=1 is

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

The tangent at P on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the asymptotes -(y)/(a)-(y^(2))/(b)=0 if the locus of the midpoint of PQ has the equation (x^(2))/(a^(2))-(y^(2))/(b^(2))=k, then k has the value equal to

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

A tangent is drawn to the ellipse to cut the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and to cut the ellipse (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 at the points P and Q. If the tangents are at right angles,then the value of ((a^(2))/(c^(2)))+((b^(2))/(d^(2))) is

The line y=x+rho (p is parameter) cuts the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at P and Q, then prove that mid point of PQ lies on a^(2)y=-b^(2)x .