Homework SourseFind the equation of the tangents to the ellipse 4x2y272 whi
Find the equation of the tangents to the ellipse 4x^2+y^2=72 which passes through the point (4,4).
Hint: notice that the pt. (4,4) is not on the ellipse. Denote the pt where the line touches the curve by (h,k) Use the data in the problem to find h and k
Hint: notice that the pt. (4,4) is not on the ellipse. Denote the pt where the line touches the curve by (h,k) Use the data in the problem to find h and k
Solution
8x + 2y y\' = 0 Let point is (h,k) 8h + 2k y\' = 0 y\' = -8h/2k = -4h/k y - k = -4h/k(x - h) yk - k^2 = 4h^2 - 4hx 4hx + yk = 72 passes through (4,4) 16h + 4k = 72 4h^2 + k^2 = 72 so h= 3 k = 6 or h = 21/5 k = 6/5
