Line `xcos alpha +y sin alpha =p` is a normal to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1 ` , if

The condition that the line x cos alpha + y sin alpha =p to be a tangent to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 is

The condition that the line x cos alpha + y sin alpha =p to be a tangent to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 is

If the line x cos alpha+ y sin alpha=p be a normal to the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2), show that, p^(2)(a^(2) sec ^(2) alpha- b^(2)"cosec"^(2) alpha)=(a^(2)+b^(2))^(2)

Find the condition for the line x cos alpha + y sin alpha = p to be tangent to the hyperbole (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

if the line x cos alpha+y sin alpha=p be a normal to the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2), shopw that,p^(2)(a^(2)sec^(2)alpha-b^(2)cos ec^(2)alpha)=(a^(2)+b^(2))^(2)

If a variable straight line x cos alpha+y sin alpha=p which is a chord of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 (b gt a) subtends a right angle at the centre of the hyperbola, then it always touches a fixed circle whose radius, is

The line x cos alpha + y sin alpha = p touches the hyperbola (x ^(2))/( a ^(2)) - (y ^(2))/( b ^(2))= 1 , if :

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

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