Question:
If a hyperbola passes through the point P(\(\sqrt{2},\sqrt{3}\)) and has foci at (±2,0), then the tangent to this hyperbola at P is
If a hyperbola passes through the point P(\(\sqrt{2},\sqrt{3}\)) and has foci at (±2,0), then the tangent to this hyperbola at P is
Updated On: Feb 15, 2024
- y=x\(\sqrt6-\sqrt3\)
- y=x\(\sqrt3-\sqrt6\)
- y=x\(\sqrt6+\sqrt3\)
- y=x\(\sqrt3+\sqrt6\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The tangent to the hyperbola at point P(2, 3/2, 3) is parallel to the x-axis.
The correct answer is option (B): y=x\(\sqrt3-\sqrt6\)
Was this answer helpful?
0
0
Top Questions on Hyperbola
- Let the foci of a hyperbola be \( (1, 14) \) and \( (1, -12) \). If it passes through the point \( (1, 6) \), then the length of its latus-rectum is:
- The foci of the hyperbola \[ 4x^2 - 9y^2 - 1 = 0 \] are:
- If \( e_1 \) and \( e_2 \) are respectively the eccentricities of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and its conjugate hyperbola, then the line \( \frac{x}{2e_1} + \frac{y}{2e_2} = 1 \) touches the circle having center at the origin, then its radius is:
- If the eccentricity of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) is \( \sec \alpha \), then the area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is:
- If \( \tanh x = \text{sech } y = \frac{3}{5} \) and \( e^{x+y} \) is an integer, then \( e^{x+y} \) is:
View More Questions
Questions Asked in WBJEE exam
- Let \(f : \mathbb{R} \to \mathbb{R}\) be given by \(f(x) = |x^2 - 1|\), then:
- \(f(x) = \cos x - 1 + \frac{x^2}{2!}, \, x \in \mathbb{R}\)
Then \(f(x)\) is: - Let \(f : \mathbb{R} \to \mathbb{R}\) be a differentiable function and \(f(1) = 4\). Then the value of
\[ \lim_{x \to 1} \int_{4}^{f(x)} \frac{2t}{x - 1} \, dt \]- WBJEE - 2024
- Integration
- If \(\int \frac{\log(x + \sqrt{1 + x^2})}{1 + x^2} \, dx = f(g(x)) + c\), then:
- WBJEE - 2024
- Integration
- The equation \(2x^5 + 5x = 3x^3 + 4x^4\) has:
- WBJEE - 2024
- Quadratic Equation
View More Questions
Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
