TS EAMCET · Maths · Pair of Lines
If \(4 x^2+12 x y+9 y^2+2 \mathrm{~g} x+2 \mathrm{f} y-1=0\) represent a pair of parallel lines then
- A \(\frac{f}{g}+\frac{g}{f}+\frac{13}{6}=0\)
- B \(\mathrm{f}^2+\mathrm{g}^2=\mathrm{fg}\)
- C \(\mathrm{f}^2+\mathrm{g}^2=6 \mathrm{fg}\)
- D \(\frac{f}{g}+\frac{g}{f}=\frac{13}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{f}{g}+\frac{g}{f}=\frac{13}{6}\)
Step-by-step Solution
Detailed explanation
Given equation: \( 4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0 \) Compare with \( (a x+b y+c_1)(a x+b y+c_2)=0 \) \( (a x+b y)^2+(c_1+c_2)(a x+b y)+c_1 c_2=0 \) \( a^2 x^2+2 a b x y+b^2 y^2+a(c_1+c_2) x+b(c_1+c_2) y+c_1 c_2=0 \) By comparing coefficients: \( a^2=4 \implies a=2 \)…
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
- If three unbiased dice are rolled simultaneously then the probability that all the three dice show distinct numbers isTS EAMCET 2023 Medium
- Consider the curves and Assertion : The common tangents to the curves and are orthogonal. Reason : and are the common tangents to the curves andTS EAMCET 2019 Medium
- A random variable takes the values and such that . If is the variance and is the mean of , thenTS EAMCET 2018 Hard
- If the equation of the circle which cuts each of the circles \(x^2+y^2=4, x^2+y^2-6 x-8 y+10=0\) and \(x^2+y^2+2 x-4 y-2=0\) at the extremities of a diameter of these circles is \(x^2+y^2+2 g x+2 f y+c=0\), then \(g+f+c=\)TS EAMCET 2024 Medium
- If the mean and variance of a binomial distribution are \(\frac{4}{3}\) and \(\frac{10}{9}\) respectively, then \(\mathrm{P}(\mathrm{X} \geq 6)=\)TS EAMCET 2025 Medium
- The general solution of the differential equation \(\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y\) isTS EAMCET 2018 Medium
More PYQs from TS EAMCET
- What is the binding energy of whose atomic mass is Mass of proton Mass of neutron (Neglect the electron mass) (Assume )TS EAMCET 2020 Easy
- If \(5 \cos x+12 \cos y=13\), then the maximum value of \(5 \sin x+12 \sin y\) is :TS EAMCET 2006 Medium
- Suppose \(\alpha, \beta, \gamma\) are the roots of \(x^3+x^2+x+2=0\). Then, the value of \(\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)\) isTS EAMCET 2015 Easy
- The equation of the circle passing through the points of intersection of the circles \(x^2+y^2+6 x+4 y-12=0\), \(x^2+y^2-4 x-6 y-12=0\) and having radius \(\sqrt{13}\) isTS EAMCET 2023 Easy
- \(\lim _{x \rightarrow \infty}\left(\frac{2 x^2+3 x+4}{x^2-3 x+5}\right)^{\frac{3|x|+1}{2|x|-1}}=\)TS EAMCET 2019 Easy
- The weight of potassium dichromate (molecular weight \(=294\) ) required to prepare \(0.04 \mathrm{~N}\) of \(250 \mathrm{~mL}\) solution isTS EAMCET 2020 Medium