In the ellipse frac{x^2}{a^2} + frac{y^2}{b^2 | vedclass

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(A) For an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,two diameters $y = m_1x$ and $y = m_2x$ are conjugate if $m_1m_2 = -\frac{b^2}{a^2}$.Given

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$y = - \frac{b}{a}x$

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(A) For an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,two diameters $y = m_1x$ and $y = m_2x$ are conjugate if $m_1m_2 = -\frac{b^2}{a^2}$.Given the diameter $y = \frac{b}{a}x$,we have $m_1 = \frac{b}{a}$.Let the conjugate diameter be $y = m_2x$.Then,$\frac{b}{a} 	imes m_2 = -\frac{b^2}{a^2}$.Solving for $m_2$,we get $m_2 = -\frac{b^2}{a^2} 	imes \frac{a}{b} = -\frac{b}{a}$.Thus,the equation of the conjugate diameter is $y = -\frac{b}{a}x$.

In the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,the equation of the diameter conjugate to the diameter $y = \frac{b}{a}x$ is:

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