Question

The image of the pair of lines represented by ${\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0$ by the line mirror $\mathrm{y}=0$ is

• A. ${\mathrm{ax}}^2–2\mathrm{hxy}–{\mathrm{by}}^2=0$
• B. ${\mathrm{bx}}^2–2\mathrm{hxy}–{\mathrm{ay}}^2=0$
• C. ${\mathrm{bx}}^2+2\mathrm{hxy}+\mathrm{ay}2=0$
• D. ${\mathrm{ax}}^2–2\mathrm{hxy}+{\mathrm{by}}^2=0$

Answer 1

The correct option is D

${\mathrm{ax}}^2–2\mathrm{hxy}+{\mathrm{by}}^2=0$

The explanation for the correct answer.

Find the mirror image of the line.

Given: ${\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0$ and $\mathrm{y}=0$.

In the mirror image, the coordinates of the x-axis become negative.

Change $\mathrm{x}$ to $-\mathrm{x}$ in the equation of a line.

We get ${\mathrm{ax}}^2-2\mathrm{hxy}+{\mathrm{by}}^2=0$

This is the image of the given line.

Hence option $\left(d\right)$ is the correct answer.