Question:
Which of the following is the equation of a hyperbola?
Which of the following is the equation of a hyperbola?
Show Hint
Hyperbola always has opposite signs for \( x^2 \) and \( y^2 \) terms.
Updated On: May 1, 2026
- \( x^2 - 4x + 16y + 17 = 0 \)
- \( 4x^2 + 4y^2 - 16x + 4y - 60 = 0 \)
- \( x^2 + 2y^2 + 4x + 2y - 27 = 0 \)
- \( x^2 - y^2 + 3x - 2y - 43 = 0 \)
- \( x^2 + 4x + 6y - 2 = 0 \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
General second-degree equation:
\[
Ax^2 + By^2 + \cdots = 0
\]
Classification:
- Ellipse: \( A, B \) same sign
- Hyperbola: \( A, B \) opposite signs
- Parabola: one of \( A \) or \( B = 0 \)
Step 1: Analyze each option.
(A), (B), (C), (E): coefficients of \( x^2 \) and \( y^2 \) have same sign or one missing → not hyperbola
Step 2: Check option (D).
\[ x^2 - y^2 + \cdots \] Coefficients have opposite signs.
Step 3: Conclude.
Hence equation represents a hyperbola.
Step 1: Analyze each option.
(A), (B), (C), (E): coefficients of \( x^2 \) and \( y^2 \) have same sign or one missing → not hyperbola
Step 2: Check option (D).
\[ x^2 - y^2 + \cdots \] Coefficients have opposite signs.
Step 3: Conclude.
Hence equation represents a hyperbola.
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM sections of a cone Questions
- Given that: \[ \frac{1}{\tan A - \tan B} = \]
- cos \( A \cos 2A \) is equal to:
- If \( y = \frac{1 + \tan^2 x}{1 - \tan^2 x} \), find \( y' \left( \frac{\pi}{8} \right) \), where \( 0<x<\frac{\pi}{4} \).
- The axis of the parabola \(x^{2} + 6x + 4y + 5 = 0\) is
- The distance between the foci of the ellipse \(\frac{(x + 2)^{2{9} + \frac{(y - 1)^{2}}{4} = 1\) is}
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions