Question 1481
CBSE Class 11 Mathematics · Straight Lines · Distance and intersections
A line has axis intercepts a and b, and p is its distance from the origin. Prove 1/p²=1/a²+1/b².
Solution to Question 1481
Complete workingTranslate every condition into an equation and retain exact values throughout the straight-line calculation.
\[\begin{aligned}\frac xa+\frac yb &= 1\Rightarrow bx+ay-ab\\&= 0\end{aligned}\]
\[p=\frac{|ab|}{\sqrt{a^2+b^2}}\]
\[\begin{aligned}\frac1{p^2} &= \frac{a^2+b^2}{a^2b^2}\\&= \frac1{a^2}+\frac1{b^2}\end{aligned}\]
The last line satisfies the original conditions and supplies every requested part.
Final answer
\[\frac1{p^2}=\frac1{a^2}+\frac1{b^2}\]