The line passing through the points (a, b) an | vedclass

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(C) Let the given points be $A(a, b)$ and $B(-a, -b)$. The slope $m$ of the line passing through $A$ and $B$ is given by: $m = \frac{y_2 - y_1}{x_2 -

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$(a^2, ab)$

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(C) Let the given points be $A(a, b)$ and $B(-a, -b)$. The slope $m$ of the line passing through $A$ and $B$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-b - b}{-a - a} = \frac{-2b}{-2a} = \frac{b}{a}$. The equation of the line passing through $(a, b)$ with slope $\frac{b}{a}$ is: $y - b = \frac{b}{a}(x - a)$ $ay - ab = bx - ab$ $bx = ay$ Now, we check the given options to see which point satisfies the equation $bx = ay$: For option $(C)$, substituting $x = a^2$ and $y = ab$: $b(a^2) = a(ab)$ $a^2b = a^2b$ Since the equation is satisfied, the line passes through $(a^2, ab)$.

The line passing through the points $(a, b)$ and $(-a, -b)$ passes through which of the following points?

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