From the point P ,the chord of contact to the ellipse `E_(1):(x^(2))/(a)+(y^(2))/(b)=(a+b)` touches the ellipse `E_(2):(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` Then the locus of point P

From a point P tangents are drawn to the elipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1.1f the chord of contact touches the ellipse (x^(2))/(c^(2))+(y^(2))/(a^(2))=1, then the locus of P is

If (x)/(a)+(y)/(b)=sqrt(2) touches the ellipses (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then fin the ecentric angle theta of point of contact

If y=mx+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then the point of contact is

If (x)/(a)+(y)/(b)=sqrt(2) touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then find the eccentric angle theta of point of contact.

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=c^(2), then the locus of the point

If the line y=x+sqrt(3) touches the ellipse (x^(2))/(4)+(y^(2))/(1)=1 then the point of contact is

If (alpha-beta)=(pi)/(2) ,then the chord joining the points whose eccentric angles are alpha and beta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(k) , then ( 5k^(2)+2) is equal to

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 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