The equations of tangents to the ellipse `9x^2+16y^2=144` from the poi – InterviewSolution

InterviewSolution

1.	The equations of tangents to the ellipse `9x^2+16y^2=144` from the point (2,3) are:
Answer» `(9x^2)/144 + (16y^2)/144 = 1` `x^2/16 + y^2/9 = 1` `(x x_1)/16 + (y y_1)/9 = 1` `x_1/8 + y_1/3 = 1` `y_1= (1- x_1/8)*3` `x^2/16 + (9/4(8-x_1)^2)/9 = 1` `x_1^2/16 + (8-x_1)^2/64 = 1` `(4x_1^2 + (8- x_1)^2)/64 = 1` `4x_1^2 + 64 - 16x_1 + x_1^2 = 64` `5x_1^2 - 16x_1 = 0` `x_1(5x_1 - 16) = 0` `x_1= 0 & x_1 = 16/5` `y_1 = 3 & y_1 = 9/5` `y=3 or x=0` `x+y = 16/5 + 9/` `x+y= 5` Answer

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