The locus of the midpoint of the system of pa | vedclass

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(B) The equation of the hyperbola is $9x^2 - 4y^2 = 36$, which can be written as $\frac{x^2}{4} - \frac{y^2}{9} = 1$. Here, $a^2 = 4$ and $b^2 = 9$. T

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$9x - 8y = 0$

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(B) The equation of the hyperbola is $9x^2 - 4y^2 = 36$, which can be written as $\frac{x^2}{4} - \frac{y^2}{9} = 1$. Here, $a^2 = 4$ and $b^2 = 9$. The slope of the parallel chords is $m = 2$. The locus of the midpoints of a system of parallel chords with slope $m$ is the diameter of the hyperbola, given by the equation $y = \frac{b^2}{a^2 m} x$. Substituting the values, we get $y = \frac{9}{4 	imes 2} x = \frac{9}{8} x$. This simplifies to $8y = 9x$, or $9x - 8y = 0$.

The locus of the midpoint of the system of parallel chords parallel to the line $y = 2x$ for the hyperbola $9x^2 - 4y^2 = 36$ is

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