AP EAMCET · Maths · Pair of Lines
If the equation
\(3 x^2+7 x y+2 y^2+2 g x+2 f y+2=0\) represents
a pair of intersecting lines and the square of the distance of their point of intersection from the origin is \(\frac{2}{5}\), then \(f^2+g^2=\)
- A \(\frac{25}{4}\)
- B 25
- C 50
- D \(\frac{25}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{25}{2}\)
Step-by-step Solution
Detailed explanation
The equation, represents a pair of intersecting lines, so \[ \begin{aligned} & \text { (3) }(2)(2)+7(g)(f)-3 f^2-2 g^2-2\left(\frac{7}{2}\right)^2=0 \\ & \Rightarrow \quad 24+14 g f-6 f^2-4 g^2-49=0 \end{aligned} \] To get the point of intersection of pair of straight lines, we…
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