Length of the chord intercepted by the ellipse $x^{2} + 4 y^{2} = 16$ , on the line $y = x \sqrt{2} + 2$ is:

\frac{16 \sqrt{5}}{3}

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\frac{16 \sqrt{6}}{9}

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\frac{12 \sqrt{3}}{5}

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\frac{14 \sqrt{3}}{5}

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Solution

The correct option is B $\frac{16 \sqrt{6}}{9}$
From the given data, we get
$x^{2} + 4 (2 x^{2} + 4 + 4 \sqrt{2} x) = 16$
$x^{2} + 8 x^{2} + 16 \sqrt{2} x = 0$
$x = 0$
$x = - \frac{16 \sqrt{2}}{9}$
$y = 2$
$y = \frac{- 32 + 18}{9}$
$y = \frac{- 14}{9}$
$v = \sqrt{(x_{1} - x_{2})^{2} + (y_{2} - y_{1})^{2}}$
$v = \sqrt{(x_{1} - x_{2})^{2} (1 + 2)}$
$= \frac{16}{9} \sqrt{6}$

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Similar questions

Verify whether the given statement is true or false :

(i) $(\frac{5}{9} \div \frac{1}{3}) \div \frac{5}{2} = \frac{5}{9} \div (\frac{1}{3} \div \frac{5}{2})$

(ii) ${(- 16) \div \frac{6}{5}} \div \frac{- 9}{10} = (- 16) \div {\frac{6}{5} \div \frac{- 9}{10}}$

(iii) $(\frac{- 3}{5} \div \frac{- 12}{35}) \div \frac{1}{14} = \frac{- 3}{5} \div (\frac{- 12}{35} \div \frac{1}{14})$

\frac{(x - 4)^{2}}{16} + \frac{(y - 3)^{2}}{9} = 1

x - y - 2 = 0

x - y = 5

\frac{x^{2}}{16} + \frac{x^{2}}{9} = 1

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

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