AP EAMCET · Maths · Pair of Lines
The transformed equation of \(3 x^2-4 x y=r^2\) when the coordinate axes are rotated about the origin through an angle of \(\operatorname{Tan}^{-1}(2)\) in positive direction is
- A \(x^2-4 y^2=r^2\)
- B \(2 x y+r^2=0\)
- C \(4 y^2-x^2=r^2\)
- D \(x y=r^2\)
Answer & Solution
Correct Answer
(C) \(4 y^2-x^2=r^2\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Tan}\theta = 2 \implies \sin\theta = \frac{2}{\sqrt{5}}, \cos\theta = \frac{1}{\sqrt{5}}\) \(x = x' \cos\theta - y' \sin\theta = \frac{x' - 2y'}{\sqrt{5}}\) \(y = x' \sin\theta + y' \cos\theta = \frac{2x' + y'}{\sqrt{5}}\)…
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
- \(\int \sin ^5 x \cdot \cos ^5 x d x=\)AP EAMCET 2019 Medium
- Let \(f: R \rightarrow R\) be defined by
\(f(x)=\left\{\begin{array}{ccc}\alpha+\frac{\sin [x]}{x}, & \text { if } & x>0 \\ 2, & \text { if } & x=0 \\ \beta+\left[\frac{\sin x-x}{x^3}\right], & \text { if } & x < 0\end{array}\right.\)
equal toAP EAMCET 2012 Easy - If \(P+Q+R=\frac{\pi}{4}\), then
\(\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos \left(\frac{\pi}{8}-R\right)=\)AP EAMCET 2024 Hard - The family of lines, forming an isosceles triangle with the lines \(3 x-4 y-2=0\) and \(12 x-5 y+6=0\), isAP EAMCET 2022 Hard
- A ray makes angles \(\frac{\pi}{3}\) and \(\frac{\pi}{4}\) with \(Y\) and \(Z\)-axes respectively. Then, the value of the sine of the angle made by the ray with \(X\)-axis isAP EAMCET 2022 Easy
- Given two points \(Q(3,4)\) and \(R(1,2)\). What is the point \(\mathrm{P}(\mathrm{x}, \mathrm{y})\) on the line \(2 \mathrm{x}-\mathrm{y}-1=0\) for which \(\mathrm{PQ}+\mathrm{PR}=\mathrm{QR}\) holdsAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- Let \(\mathrm{A}=(-3,-2,7)\) and \(\mathrm{B}=(3,1,-2)\). Let a plane perpendicular to the line segment \(A B\) divide \(A B\) in the ratio \(2: 1\). Then the intercept made by the plane on \(y\)-axis isAP EAMCET 2022 Medium
- A ball at rest is dropped from a height of 12 . It losses \(25 \%\) of its kinetic energy on striking the ground and bounces back to a height ' \(h\) '. Then value of ' \(h\) ' isAP EAMCET 2013 Medium
- A ray of light is incident on the surface of a glass plate of refractive index \(\sqrt{3}\) at the polarising angle. The angle of refraction of the ray isAP EAMCET 2019 Easy
- The triple point of water isAP EAMCET 2020 Easy
- One of the two identical capacitors having the same capacitance C, is charged to a potential \(\mathrm{V}_1\) and the other is charged to a potential \(\mathrm{V}_2\). If they are connected with their like plates together, then the decrease in the electrostatic potential energy of the combined system isAP EAMCET 2025 Medium
- A vector of magnitude \(\sqrt{51}\) which makes equal angles with the vectors \(\bar{a}=\frac{1}{3}(\bar{i}-2 \bar{j}+2 \bar{k})\), \(\bar{b}=\frac{1}{5}(-4 \bar{i}-3 \bar{k})\) and \(\bar{c}=\bar{j}\), isAP EAMCET 2017 Medium