Question

If the distance from the origin to the line ax+by+5=0 is 5/root10,then the distance from the origin to the line ax+by+10=0 is

Answer 1

Distance of a straight line from a point

If $d$ be the distance of a straight line $ax+by+c=0$ from a point with coordinates $(x_{1},\:y_{1})$, then we have

• $d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^{2}+b^{2}}}$

Given: the distance from the origin to the line $ax+by+5=0$ is $\frac{5}{\sqrt{10}}$

To find: the distance from the origin to the line $ax+by+10=0$

Solution:

• The distance from the origin to the line $ax+by+5=0$ is

• $=\frac{5}{\sqrt{a^{2}+b^{2}}}$

• Given, $\frac{5}{\sqrt{a^{2}+b^{2}}}=\frac{5}{\sqrt{10}}$

• $\Rightarrow \sqrt{a^{2}+b^{2}}=\sqrt{10}$

• Now the distance from the origin to the line $ax+by+10=0$ is

• $=\frac{10}{\sqrt{a^{2}+b^{2}}}$

• $=\frac{10}{\sqrt{10}}$ [ from above ]

• $=\sqrt{10}$ units

Answer: the distance from the origin to the line $ax+by+10=0$ is $\sqrt{10}$ units.