If the line `x cos alpha+y sin alpha=p` touches the ellipse `x^(2)/a^(2)+(y^(2))/(b^(2))=1` then the point of contact will be

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

If the line x cos alpha+y sin alpha=P touches the curve 4x^(3)=27ay^(2), then (P)/(a)=

The portion of the line x cos alpha+y sin alpha=p intercepted by the ellipse- (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 subtends a right angle at the centre of the ellipse.Prove that the line touches a circle concentric with the ellipse.

If the straight line x cos alpha+y sin alpha=p touches the curve (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, then prove that a^(2)cos^(2)alpha-b^(2)sin^(2)alpha=p^(2)

If the straight line x cos alpha+y sin alpha=p touches the curve (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, then prove that a^(2)cos^(2)alpha+b^(2)sin^(2)alpha=p^(2)

The line x cos alpha + y sin alpha +y sin alpha =p is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. if

If the line 3x+4y=sqrt(7) touches the ellipse 3x^(2)+4y^(2)=1, then the point of contact is