WBJEE · Maths · Trigonometric Ratios & Identities
The equation \(r^2 \cos ^2\left(\theta-\frac{\pi}{3}\right)=2\) represents
- A a parabola
- B a hyperbola
- C a circle
- D a pair of straight lines
Answer & Solution
Correct Answer
(D) a pair of straight lines
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Hint: } r^2\left(\frac{\cos \theta}{2}+\frac{\sqrt{3}}{2} \sin \theta\right)^2=2 \\ & \Rightarrow \quad(r \cos \theta+\sqrt{3} r \sin \theta)^2=8 \\ & \Rightarrow \quad(x+y \sqrt{3})^2=8 \\ & \Rightarrow \quad(x+y \sqrt{3}-2 \sqrt{2})(x+y \sqrt{3}+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
- The line \(y-\sqrt{3} x+3=0\) cuts the parabola \(y^2=x+2\) at the points \(P\) and \(Q\). If the co-ordinates of the point \(X\) are \((\sqrt{3}, 0)\), then the value of \(X P \cdot X Q\) isWBJEE 2025 Medium
- The integrating factor of the differential equation \(x \log x \frac{d y}{d x}+y=2 \log x\) is given byWBJEE 2009 Medium
- The general value of the real angle \(\theta\), which satisfies the equation. \((\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots(\cos n \theta+t \sin n \theta)=1\) is given by, (assuming \(k\) is an integer)WBJEE 2019 Medium
- The co-efficient of \(a^{3} b^{4} c^{5}\) in the expansion of \((b c+c a+a b)^{6}\) isWBJEE 2021 Medium
- The locus of the mid-points of the chords of the circle \(x^{2}+y^{2}+2 x-2 y-2=0,\) which make an angle of \(90^{\circ}\) at the centre isWBJEE 2017 Hard
- The general solution of the differential equation \(\log _{\mathrm{e}}\left(\frac{d y}{d x}\right)=x+y\) isWBJEE 2011 Easy
More PYQs from WBJEE
- The value of \(K\) in order that \(f(x)=\sin x-\cos x-K x+5\) decreases for all positive real values of \(x\) is given byWBJEE 2017 Medium
- A bullet of mass \(m\) travelling with a speed \(v\) hits a block of mass \(M\) initially at rest and gets embedded in it. The combined system is free to move and there is no other force acting on the system. The heat generated in the process will beWBJEE 2013 Easy
- A uniform long tube is bent into a circle of radius \(\mathrm{R}\) and it lies in vertical plane. Two liquids of same volume but densities \(\rho\) and \(\delta\) fill half the tube. The angle \(\theta\) is
WBJEE 2010 Hard - Consider the function f(x) = x(x - 1) (x - 2) ... (x - 100). Which one of the following is correct?WBJEE 2024 Easy
- The co-ordinate of a point on the auxiliary circle of the ellipse \(x^{2}+2 y^{2}=4\) corresponding to the point on the ellipse whose eccentric angle is \(60^{\circ}\) will beWBJEE 2021 Easy
- If \(y=\tan ^{-1} \sqrt{\frac{1-\sin x}{1+\sin x}}\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\pi}{6}\) isWBJEE 2009 Hard