JEE Main 2021MathematicsCircleChord With A Given Middle PointhardMCQ
JEE Main 2021 — Circle Question with Solution
From: JEE Main 2021 (Online) 26th August Morning Shift
Question
If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point (−30, 0) and is tangent to the parabola y2 = 30x, then the length of this chord is :
Choose an option
▸Show full solutionCorrect option: D
Correct answer
D35
Step-by-step explanation
Equation of tangent to y2 = 30 x
y = mx + 4m30
Pass thru (−30, 0) : a = −30m + 4m30⇒ m2 = 1/4
⇒ m = 21 or m = −21
At m = 21 : y = 2x + 15 ⇒ x − 2y + 30 = 0
lAB = 2R2−P2 = 24225−5225
⇒ lAB = 30 . 201 = 515 = 35
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