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+n=0 touches the circle x^2+y^2=a^2 , then prove that (l^2+m^2)a^2=n^2dot

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

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

If x/alpha+y/beta=1 touches the circle x^2+y^2=a^2 then point (1/alpha , 1/beta) lies on (a) straight line (b) circle (c) parabola (d) ellipse

If x/alpha+y/beta=1 touches the circle x^2+y^2=a^2 then point (1/alpha , 1/beta) lies on (a) straight line (b) circle (c) parabola (d) ellipse

If the line 2x-y+1=0 touches the circle at the point (2,5) and the centre of the circle lies in the line x+y-9=0. Find the equation of the circle.

A line L is perpendicular to the line 3x-4y-7=0 and touches the circle x^(2)+y^(2)-2x-4y-4=0 , the y -intercept of the line L can be:

A line L is perpendicular to the line 3x-4y-7=0 and touches the circle x^(2)+y^(2)-2x-4y-4=0 , the y -intercept of the line L can be:

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 ?

Show that the line 5x + 12y - 4 = 0 touches the circle x^(2)+ y^(2) -6x + 4y + 12 = 0