WBJEE · Maths · Pair of Lines
The equation \(8 x^2+12 y^2-4 x+4 y-1=0\) represents
- A an ellipse
- B a hyperbola
- C a parabola
- D a circle
Answer & Solution
Correct Answer
(A) an ellipse
Step-by-step Solution
Detailed explanation
Hints: \(a x^2+b y^2+2 h x y+2 g x+2 f y+c=0\) represents ellipse if \(\mathrm{h}^2-a b < 0\) \(\begin{aligned} & 3 x^2+12 y^2-4 x+4 y-1=0 \\ & h=0, a=3, b=12 \\ & h^2-a b < 0 \end{aligned}\)
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 \(\alpha\) and \(\beta\) are the roots of \(x^{2}-p x+1=0\) and \(\gamma\) is a root of \(x^{2}+p x+1=0,\) then \((\alpha+\gamma)(\beta+\gamma)\) isWBJEE 2015 Medium
- The quadratic equation \(x^2+15|x|+14=0\) hasWBJEE 2010 Easy
- \(\int \frac{d x}{x(x+1)}\) equals
where \(c\) is an arbitrary constant.WBJEE 2009 Medium - The quadratic equation
\(2 x^{2}-\left(a^{3}+8 a-1\right) x+a^{2}-4 a=0\) has roots of opposite sign. Then,WBJEE 2012 Medium - If \(f(x)=\int_{-1}^{x}|t|\) dt, then for any \(x \geq 0, f(x)\) is equal toWBJEE 2017 Easy
- Let \(\rho\) be a relation defined on \(N\), the set of natural numbers, as \(\rho=\{(x, y) \in N \times N: 2 x+y=41\} .\) ThenWBJEE 2018 Easy
More PYQs from WBJEE
- Let \(f(n)=2^{n+1}, g(n)=1+(n+1)^{2 n}\) for all \(n \in \mathbb{N}\). ThenWBJEE 2022 Medium
- The value of \(\cos ^{2} 75^{\circ}+\cos ^{2} 45^{\circ}+\cos ^{2} 15^{\circ}\) \(-\cos ^{2} 30^{\circ}-\cos ^{2} 60^{\circ}\) isWBJEE 2013 Easy
- Let \(A\) and \(B\) be two events such that \(P(A \cap B)=\frac{1}{6}, P(A \cup B)=\frac{31}{45}\) and \(P(\bar{B})=\frac{7}{10}\) thenWBJEE 2016 Medium
- If \(\cos x\) and \(\sin x\) are solutions of the differential equation \(a_{0} \frac{d^{2} y}{d x^{2}}+a_{1} \frac{d y}{d x}+a_{2} y=0\) where \(a_{0}, a_{1}\) and \(a_{2}\) are real constants, then which of the following is/are always true?WBJEE 2015 Medium
- In open interval \(\left(0, \frac{\pi}{2}\right)\),WBJEE 2020 Medium
- The point \(P(3,6)\) is first reflected on the line \(y=x\) and then the image point \(Q\) is again reflected on the line \(y=-x\) to get the image point \(Q^{\prime} .\) Then, the circumcentre of the \(\Delta P Q Q^{\prime}\) isWBJEE 2017 Hard