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

Explanation

`x+y=5, y=3 `

`9 x^{2}+16 y^{2}=144 `

`Rightarrow frac{x^{2}}{16}+frac{y^{2}}{9}=1`

Equation of tangent in case of an ellipse is

`y=m x+sqrt{a^{2} m^{2}+b^{2}} `

`Rightarrow y=m x+sqrt{16 m^{2}+9} ldots .(1)`

Substituting `x=2` and `y=3`

`3=2 m pm sqrt{16 m^{2}+9} `

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