First slide

Ellipse

Question

The straight line $x + y = k$ will be a tangent to the curve $16 x^{2} + 9 y^{2} = 144,$ if $k =$

Easy

A

$\pm 8$
B

$\pm 5$
C

$\pm 10$
D

$\pm 4$

Solution

$16 x^{2} + 9 y^{2} = 144 ............ (1)$
$x + y = k ................ (2)$
If $y = m x + c$ is tangent of equation $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$
Then $\begin{matrix} c^{2} = a^{2} m^{2} + b^{2} \end{matrix}$
$a^{2} = 9, b^{2} = 16, m = - 1$
$\begin{matrix} \end{matrix} \Rightarrow k^{2} = 9 + 16 = 25$
$k = \pm 5$

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