Mathematics · 2021
JEE Main · 25 February 2021, Shift 2 · Q89
A line is a common tangent to the circle (x-3)^2+y^2=9 and the parabola y^2=4 x. If the two points of contact (a, b) and (c, d) are distinct and lie…
A line is a common tangent to the circle $\displaystyle (x-3)^2+y^2=9$ and the parabola $\displaystyle y^2=4 x$. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then $\displaystyle 2(\mathrm{a}+\mathrm{c})$ is equal to \_\_\_\_.
Official answer
9
More from Parabola
- Let the tangent to the curve x^2+2 x-4 y+9=0 at the point P(1,3) on it meet the y -axis at A. Let the line passing through P and parallel to the line…2023
- The ordinates of the points P and Q on the parabola with focus (3,0) and directrix x=-3 are in the ratio 3: 1. If R(α, β) is the point of…2023
- The tangents at the points A(1,3) and B(1,-1) on the parabola y^2-2 x-2 y=1 meet at the point P. Then the area (in unit ^2 ) of the triangle P A B is:2022
- Two parabolas have the same focus (4,3) and their directrices are the x -axis and the y -axis, respectively. If these parabolas intersects at the…2025
- Let a line y=m x( m>0) intersect the parabola, y^2=x at a point P, other than the origin. Let the tangent to it at P meet the x -axis at the point Q.…2020
- Let the image of parabola x^2=4 y, in the line x-y=1 be (y+a)^2=b(x-c), a, b, c ∈ N. Then a+b+c is equal to2026
- Let P(α, β) be a point on the parabola y^2=4 x. If P also lies on the chord of the parabola x^2=8 y whose mid point is (1, 5/4), then (α-28)(β-8) is…2024
- Let P_1 be a parabola with vertex (3,2) and focus (4,4) and P_2 be its mirror image with respect to the line x+2 y=6. Then the directrix of P_2 is…2022
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.