Question

The line through the points $(a,b)$ and $(-a,-b)$ passes through the point

• A. $(1,1)$
• B. $(3a,-2b)$
• C. $(a^2,ab)$
• D. $(4a,2b)$

Answer 1

Answer: (C)

$(a^2,ab)$

Slope of line passing through $(a,b)$ and $(-a,-b)$ is given by $\frac{b+b}{a+a}=\frac{b}{a}$

So equation of line passing is given by (using slope point form)

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

$\Rightarrow ay-ab=bx-ab$

$\Rightarrow ay=bx$

Clearly the point $(a^2,ab)$ lie on the above line

Hence option $C$ is correct choice