Question

The equations of tangents to the ellipse `9x^2+16y^2=144` from the point (2,3) are:

Answer 1

`(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