Mathematics · 2023
JEE Main · 31 January 2023, Shift 2 · Q75
The set of all values of a^2 for which the line x+y=0 bisects two distinct chords drawn from a point P ((1+a)/2, (1-a)/2) on the circle 2 x^2+2…
The set of all values of $\displaystyle a^2$ for which the line $\displaystyle x+y=0$ bisects two distinct chords drawn from a point $\displaystyle \mathrm{P}\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $\displaystyle 2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :
Official answer
From NTA’s final answer key for this paper.
(2)
$\displaystyle (8, \infty)$
More from Circle
- A circle passing through the point P(α, β) in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line…2023
- Consider the circle C: x^2+y^2-6 x-8 y-11=0. Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of…2026
- Let the circle x^2+y^2=4 intersect x -axis at the points A(a, 0), a>0 and B(b, 0). Let P(2 cos α, 2 sin α), 0<α<(π)/2 and Q(2 cos β, 2 sin β) be two…2026
- A line segment AB of length λ moves such that the points A and B remain on the periphery of a circle of radius λ. Then the locus of the point, that…2023
- Let the line L: √2 x+y=α pass through the point of the intersection P (in the first quadrant) of the circle x^2+y^2=3 and the parabola x^2=2 y. Let…2024
- Let PQ and MN be two straight lines touching the circle x^2+y^2-4 x-6 y-3=0 at the points A and B respectively. Let O be the centre of the circle and…2026
- The number of common tangents, to the circles x^2+y^2-18 x-15 y+131=0 and x^2+y^2-6 x-6 y-7=0, is2023
- Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3,2) and parallel to the coordinate axes touch…2024
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.