Mathematics · 2020
JEE Main · 2 September 2020, Shift 1 · Q65
A line parallel to the straight line 2 x-y=0 is tangent to the hyperbola x^2/4-y^2/2=1 at the point (x_1, y_1). Then x_1^2+5 y_1^2 is equal to:
A line parallel to the straight line $\displaystyle 2 x-y=0$ is tangent to the hyperbola $\displaystyle \frac{x^2}{4}-\frac{y^2}{2}=1$ at the point $\displaystyle \left(x_1, y_1\right)$. Then $\displaystyle x_1^2+5 y_1^2$ is equal to :
Official answer
(3)
$\displaystyle 6$
More from Hyperbola
- Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding…2025
- A hyperbola passes through the foci of the ellipse x^2/25+y^2/16=1 and its transverse and conjugate axes coincide with major and minor axes of the…2021
- If A and B are the points of intersection of the circle x^2+y^2-8 x=0 and the hyperbola x^2/9-y^2/4=1 and a point P moves on the line 2 x-3 y+4=0,…2025
- Let the equation of two diameters of a circle x^2+y^2-2 x+2 f y+1=0 be 2 p x-y=1 and 2 x+p y=4 p. Then the slope m ∈(0, ∞) of the tangent to the…2022
- The locus of the centroid of the triangle formed by any point P on the hyperbola 16 x^2-9 y^2+32 x+36 y-164=0, and its foci is:2021
- Let a>0, b>0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola x^2/(a^2)-y^2/(b^2)=1. Let e^′ and l^′…2022
- Let x^2/(a^2)+y^2/(b^2)=1, a>b be an ellipse, whose eccentricity is 1/(√2) and the length of the latusrectum is √14. Then the square of the…2024
- Let the tangent drawn to the parabola y^2=24 x at the point (α, β) is perpendicular to the line 2 x+2 y=5. Then the normal to the hyperbola…2022
JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.