Question:
The equation $x=\frac{e^t\,+\,e^{-t}}{2};y=\frac{e^1\,-\,e^{-t}}{2};t\in$ R represents
The equation $x=\frac{e^t\,+\,e^{-t}}{2};y=\frac{e^1\,-\,e^{-t}}{2};t\in$ R represents
Updated On: Jul 5, 2022
- an ellipse
- a parabola
- a hyperbola
- a circle.
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Answer (c) a hyperbola
Was this answer helpful?
0
0
Top Questions on Conic sections
- Let \[ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. \] Let the distance between the foci of \( E \) and the foci of \( H \) be \( 2\sqrt{3} \). If \( a - A = 2 \), and the ratio of the eccentricities of \( E \) and \( H \) is \( \frac{1}{3} \), then the sum of the lengths of their latus rectums is equal to:
- JEE Main - 2025
- Mathematics
- Conic sections
- Let \[ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. \] Let the distance between the foci of \( E \) and the foci of \( H \) be \( 2\sqrt{3} \). If \( a - A = 2 \), and the ratio of the eccentricities of \( E \) and \( H \) is \( \frac{1}{3} \), then the sum of the lengths of their latus rectums is equal to:
- JEE Main - 2025
- Mathematics
- Conic sections
If a tangent to the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of such tangent with the positive slope is:
- AP EAPCET - 2024
- Mathematics
- Conic sections
If a circle of radius 4 cm passes through the foci of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and is concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is:
- AP EAPCET - 2024
- Mathematics
- Conic sections
- If the ellipse \(4x^2 + 9y^2 = 36\) is confocal with a hyperbola whose length of the transverse axis is 2, then the points of intersection of the ellipse and hyperbola lie on the circle:
- AP EAMCET - 2024
- Mathematics
- Conic sections
View More Questions