The equation of the diameter of the ellipse x2a2+y2b2=1 is.

A
$y = \frac{b^{2} x}{a^{2} m}$
B
$y = - \frac{b^{2} x}{a^{2} m}$
C
$y = - \frac{b^{2} x}{a^{2} n}$
D
$y = - \frac{b^{2} y}{a^{2} m}$

Solution:

Let $(h, k)$ be the mid-point of the chord $y = m x + c$ ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ .

Then $T = S_{1}$

$\begin{array}{l} \Rightarrow \frac{x h}{a^{2}} + \frac{y k}{b^{2}} = \frac{h^{2}}{a^{2}} + \frac{k^{2}}{b^{2}} \\ \Rightarrow k = - \frac{b^{2} h}{a^{2} m} \end{array}$

Hence, the locus of the mid-point is $y = - \frac{b^{2} x}{a^{2} m}$

The equation of the diameter of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is.

Solution:

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