AP EAMCET · Maths · Pair of Lines
\[
\begin{aligned}
& \text { If the } \\
& a x^2+2 h x y+b y^2+2 g x+2 f y+c=0
\end{aligned} \text { equation }
\]
represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is
- A \(\frac{c(a+b)-a f^2-b g^2}{a b-h^2}\)
- B \(\frac{c(a+b)+f^2+g^2}{a b-h^2}\)
- C \(\frac{c(a+b)-f^2-g^2}{a b-h^2}\)
- D \(\frac{c(a+b)-f^2-g^2}{\left(a b-h^2\right)^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{c(a+b)-f^2-g^2}{a b-h^2}\)
Step-by-step Solution
Detailed explanation
We know that the point of intersection of the pair of straight line is \[ \left(\sqrt{\frac{f^2-b c}{h^2-a b}}, \sqrt{\frac{g^2-a c}{h^2-a b}}\right) \] Required distance…
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