Question:
If a normal chord at a point "t" on the parabola $y^2 = 4ax$ subtends a right angle at the vertex, then t =
If a normal chord at a point "t" on the parabola $y^2 = 4ax$ subtends a right angle at the vertex, then t =
Updated On: Jul 5, 2022
- 1
- $\sqrt{2}$
- 2
- $\sqrt{3}$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Normal chord at a point $'t'$ on the parabola $y^2 = 4 \,ax$ subtends a right angle at the vertex.
$\Rightarrow t^2 = 2$
$\Rightarrow t = \sqrt 2 $
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