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

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

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

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 line x cos alpha + y sin alpha = p " touches circle " x^(2) + y^(2) =2ax then p =

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

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 ((-a^(2)cos alpha)/(p),(-b^(2)sin alpha)/(p)) ((b^(2)cos alpha)/(p),(a^(2)sin alpha)/(p)) ((b^(2)sin alpha)/(p),(a^(2)cos alpha)/(p)) ( (a^(2)cos alpha)/(p),(b^(2)sin alpha)/(p))

The line x sin alpha - y cos alpha =a touches the circle x ^(2) +y ^(2) =a ^(2), then,

Show that the straight line x cos alpha+y sin alpha=p touches the curve xy=a^(2), if p^(2)=4a^(2)cos alpha sin alpha