For what value of c, the straight line 3x + y - c = 0 touches the circle x`^2` + y`^2` + 2x - 6y + 6 = 0 ?

Show that the straight line 3x + 4y = 20 touches the circle x ^2 + y ^2 = 16.

Find the value of k for which the line x + 2y + k = 0 touches the circle x ^2 + y ^2 = 5.

For what value of k,the lines 3x+2y-4=0 and kx-4y+5=0 are parallel?

For what value of p,y = x + p touches the ellipse 2x ^2 + 3y ^2 = 1 ?

For what valu of k, y = 2x + 1 touches y ^2 = kx?

Find the equation of the circle whose radius 4 and which is concentric with the circle x ^2 + y ^2 + 2x - 6y = 0.

Without solving the equations show that the straight lines 4x - y + 2 = 0, 3x + 2y -1 = 0 and x - 3y + 3 = 0 are concurrent.

Show that x + y = 1 is the equation of the line of a diameter of the circle x ^2 + y ^2 - 4x + 2y + 1 = 0

Find the equation of the circle of radius 5 units which is concentric with the circle x ^2 + y ^2 + 2x - 4y = 0

Find the equation of straight line passing through the point of intersection of the straight lines 2x - 3y + 4 = 0 and x + 2y - 5 = 0 and perpendicular to the line 3x - 4y + 5 = 0.