If the line `p x + qy = 1` touches the circle `x^2 + y^2 = r^2,` prove that the point `(p, q)` lies on the circle `x^2 + y^2 = r^-2.`

If lx+my=1 touches the circle x^(2)+y^(2)=a^(2) , prove that the point (l,m) lies on the circle x^(2)+y^(2)=a^(-2)

If lx+my=1 touches the circle x^(2)+y^(2)=a^(2) , prove that the point (l,m) lies on the circle x^(2)+y^(2)=a^(-2)

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

Slope of tangent to the circle (x-r)^(2)+y^(2)=r^(2) at the point (x.y) lying on the circle is

The line y=x+asqrt2 touches the circle x^2+y^2=a^2 at P. The coordinate of P are

There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9 , then the value of r_(1)^(2) + r_(2)^(2) is.

A straight line x=y+2 touches the circle 4(x^(2)+y^(2))=r^(2), The value of r is: