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?

The line y = x + 8 touches the cllipse x ^2 /a ^2 + y ^2 /b ^2 = 1 whose eccentricity is sqrt2 /3. Find a and b.

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

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 ?

For what value of p the system equations, px-y=2, 6x-2y=3 has only one solution?

Find the equation of the tangents to the ellipse 3x ^2 + 4y ^2 = 12 which are perpendicular to the line 2x +y - 4 = 0.

Find the equation of the tangents drawn from the point (2, 3) to the ellipse 9x ^2 + 16y ^2 = 144.

Find the value of p, so that the lines (1 -x)/(3) = ( 7y - 14)/(2p) = ( z -3)/( 2) and ( 7-7x)/(3p) = ( y-5)/(1) = ( 6 - z)/(5) are intersect each other are right angle.