Question

Find the equations of the tangents drawn from the point (2, 3) to the ellipse `9x^2+16 y^2=144.`

Answer 1

Given ellipse is `(x^(2))/(16)+(y^(2))/(9)=1`
Let the equation of tangent by `y=mx+sqrt(16m^(2)+9)`
It passes through the point (2,3) .
`:. 3=2m+sqrt(16m^(2)+9)`
`rArr (3-2m)^(2)=16m^(2)+9`
`rArr12m^(2)+12m=0`
`rArrm=0,-1`
Therefore, equation of tangents are
`y-3=-1(x-2) and y-3=0`
`o y=-x+5 and y=3`