EllipseHardBloom L3
Question
Equation of tangents drawn from $(2,3)$ to the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ is/are:
Options
A.$x + y + 5 = 0$
B.$x + y - 5 = 0$
C.$y + 3 = 0$
D.$y - 3 = 0$
Solution
Sol. Equation of tangent is
$$y = mx \pm \sqrt{16m^{2} + 9}$$
Put $(2,3)$
$$\begin{matrix} & \ \Rightarrow \ (3 - 2m)^{2} = 16m^{2} + 9 \\ & \ \Rightarrow \ 12m^{2} + 12m = 0 \\ & \ \Rightarrow \ m = 0, - 1 \end{matrix}$$
$\therefore\ $ Tangents are $y = 3,y - 3 = - 1(x - 2)y = 3$ and $y + x = 5$
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