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

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

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 p,y = x + p touches the ellipse 2x ^2 + 3y ^2 = 1 ?

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

Prove that the straight lines y - x + 1 = 0, 2y - x - 1 = 0 and 7x -y - 19 = 0 are concurrent.

Factorise : 9x^2y^2 - 16

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

A straight line passes through the point of intersection of the straight lines 3x - 2y + 4 = 0 and 2x + 3y +5 = 0 and is parallel to the straight line x -y + 5 = 0. Find its equation.