Question

Reduce the equation $8x+9y-2=0$ to intercept form.Hence find the length of the segment intercepted between the axes.

Answer 1

The given equation is $8x+9y-2=0$

$\Rightarrow$8x+9y=2$

Dividing both sides by $2$, we get

$\Rightarrow \frac{8x}{2}+\frac{9y}{2}=1$

$\Rightarrow \frac{x}{\frac{1}{4}}+\frac{y}{\frac{2}{9}}=1$ which is the required intercept form.

Here $x-$intercept$=a=\frac{1}{4}$ and $x-$intercept$=b=\frac{2}{9}$

$\therefore$The length of the segment intercepted between the axes$=\sqrt{a^2+b^2}$

$=\sqrt{{\left(\frac{1}{4}\right)}^2+{\left(\frac{2}{9}\right)}^2}$

$=\sqrt{\frac{1}{16}+\frac{4}{81}}$

$=\sqrt{\frac{81+64}{16\times 81}}$

$=\frac{\sqrt{145}}{4\times 9}$

$=\frac{\sqrt{145}}{36}$ units