Verified answer

The conic is a circle center (0,0) and radius √p.

The perpendicular distance from (0,0) to the line

x cosα + y sinα - p =0 is

p/√( cos²α + sin²α) = p

This should equal the radius, so the line is not a tangent to the conic.

It is not clear what is wanted in the question.

You could solve the two equations simultaneously getting (say) a quadratic

equation for x which involves p and α. The line will be a tangent if the

equation has equal roots. The algebra is not very nice.

x^2+y^2=p

centre of the circle (0,0),radius of the circle=p

if the line x cosA+y sinA=p touches the above circle

than perpendicular drawn from the centre of the circle

will be equal to radius of the given circle

P=Modulous[(0.cosA+0.sinA -p)/sqrt(cos^2A+sin^2S)]=p

P=p=Radius of the circle

hence the given line touches the above circle