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 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 lines 5x + 4y - 6 = 0 and 2x + ky + 9 = 0 are (ii) perpendicular.

Find the value of k for which the lines 5x + 4y - 6 = 0 and 2x + ky + 9 = 0 are (i) parailel,

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

Find the value of k for which the pair of linear equation kx+3y=k-2 and 12x+ky=k has no solution.

Find the values of k for which the following system of equations has non-trivial solution. : 2x+3y-2z=0, 2x-y+3z=0, 7x+ky-z=0

Find the equation of the circle whose centre is (2, 3) and which touches the line 3x - 4y - 1 = 0.

Find the value of k for which f(x)={(2x+k,0lexle 1),(3x, x>1):}, "" is continuous at x=1