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I need to find the equations of the tangents to the ellipse 4x^2 + y^2 =...

I need to find the equations of the tangents to the ellipse 4x^2 + y^2 = 72 which pass through the point (4,4). Seeing that (4,4) is not on the ellipse, I need to find the equations of the tangents by denoting the unknown point by (h, k). I used implicit differentiation and found dy/dx = -4x/y and used that to denote the slope, letting m = -4h/k. Now, when I substitute m into point slope form I get a curve, not a straight line, which tells me I am doing something wrong. I have 4-k = -4h/k(4-h). Can someone help me solve for (h, k)?

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