TS 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…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(f(x)=x^2+a x+b\), where \(a, b \in R\). If \(f(x)=0\) has all its roots imaginary, then the roots of \(f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=0\) areTS EAMCET 2009 Easy
- For the hyperbola \(x^2-y^2-4 x+2 y+c=0\), if the focus is \(S(2+2 \sqrt{2}, k)\) and the directrix that is adjacent to \(S\) is \(x=2+\sqrt{2}\), then \(c=\)TS EAMCET 2020 Medium
- The angle between the tangents drawn from the point \((1,4)\) to the parabola \(y^2=4 x\) isTS EAMCET 2019 Easy
- \(\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}\) is equal toTS EAMCET 2010 Easy
- Two ships leave a port from a point at the same time. One goes with a velocity of \(3 \mathrm{~km} / \mathrm{h}\) along North-East maling an angle of \(45^{\circ}\) with East direction and the other travels with a velocity of \(4 \mathrm{~km} / \mathrm{h}\) along South-East maling an angle of \(15^{\circ}\) with East direction. Then, the distance between the ships at the end of two hours isTS EAMCET 2018 Medium
- \(\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}\) is equal toTS EAMCET 2008 Medium
More PYQs from TS EAMCET
- \(\lim _{x \rightarrow 0} x^2 \sin \frac{\pi}{x}\) is equal toTS EAMCET 2005 Easy
- If is the angle between the lines joining the origin to the points of intersection of the curve and the line thenTS EAMCET 2019 Easy
- If \(f:[a, b] \rightarrow[c, d]\) is a continuous and strictly increasing function, then \(\frac{d-c}{b-a}\) isTS EAMCET 2025 Medium
- Iron sulphide is heated in air to form \(A\) an oxide of sulphur. \(A\) is dissolved in water to give an acid. The basicity of this acid isTS EAMCET 2002 Easy
- In a nuclear reactor, the main purpose of the moderator is toTS EAMCET 2021 Medium
- If \(Z=x+i y\) is a complex number and \(\sqrt{x^2-2 x+8}+(x+4) i=y(2+i)\), then \(Z\) is equal toTS EAMCET 2021 Easy