True or False:
If the line `lx + my = 1` touches the circle `x^2 + y^2 =a^2`, then the point `(l,m) `lies on the circles.

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)

The line 4y - 3x + lambda =0 touches the circle x^2 + y^2 - 4x - 8y - 5 = 0 then lambda=

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 . Find the coordinates of the point of contact.

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

True or false The line x=y=z lies in the plane x-2y+z-1=0.

If the straight line ax + by = 2 ; a, b!=0 , touches the circle x^2 +y^2-2x = 3 and is normal to the circle x^2 + y^2-4y = 6 , then the values of 'a' and 'b' are ?

If the point (1, 4) lies inside the circle x^(2)+y^(2)-6x-10y+p=0 then p is:

If the chord of contact of the tangents drawn from a point on the circle x^2+y^2=a^2 to the circle x^2+y^2=b^2 touches the circle x^2+y^2=c^2 , then prove that a ,b and c are in GP.

Find the equation of the circle whose radius is 5 and which touches the circle x^2 + y^2-2x- 4y- 20 = 0 externally at the point (5, 5).