coorrdinate geometry(find gradient and prove)

a) Prove that if the line lx + my + n =0 touches the ellipse b^2 x^2 + a^2 y^2= a^2 b^2 , then a^2 l^2 +b^2 m^2 = n^2

b) If m is the gradient of the tangent from the point (3,2) to the ellipse 9x^2+16y^2=144, , find a quadratic equation in m .by nothing whether the roots of this equation are real or imaginary ,determine if the point (3,2) lies within the ellipse.

c) Find the gradient of the tangents drawn from the point (4,6) to the ellipse x^2+12y^2=48. Hence ,find the equation of the tangents and their points of contact with the ellipse.