JEE Main 2021 — Parabola Question with Solution
From: JEE Main 2021 (Online) 25th February Evening Shift
Question
A line is a common tangent to the circle (x 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a + c) is equal to _________.
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Show full solutionCorrect answer: 9
Correct answer
9
Step-by-step explanation
Circle : (x 3)2 + y2 = 9
Parabola : y2 = 4x
Let tangent y = mx +
y = mx +
m2x my + 1 = 0
the above line is also tangent to circle
(x 3)2 + y2 = 9
from (3, 0) = 3
(3m2 + 1)2 = 9(m2 + m4)
tangent is
(it will be used)
or
(rejected)
For parabola
= (c, d)
for circle
&
Solving,
Parabola : y2 = 4x
Let tangent y = mx +
y = mx +
m2x my + 1 = 0
the above line is also tangent to circle
(x 3)2 + y2 = 9
from (3, 0) = 3
(3m2 + 1)2 = 9(m2 + m4)
tangent is
(it will be used)
or
(rejected)
For parabola
= (c, d)
for circle
&
Solving,
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