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JEE Main 2021 · Mathematics · Straight Lines and Circles · medium

The length of the chord intercepted by the line 3x+4y=3 on the circle x^2+y^2-4x-6y-12=0 is

Single correct option

The length of the chord intercepted by the line 3x+4y=33x+4y=3 on the circle x2+y2−4x−6y−12=0x^2+y^2-4x-6y-12=0 is
  1. A. 55
  2. B. 66
  3. C. 88
  4. D. 1010
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Answer: (C) 88

The circle has centre (2,3)(2,3) and radius 4+9+12=5\sqrt{4+9+12}=5. The distance of the centre from the line is ∣6+12−3∣5=3\dfrac{|6+12-3|}{5}=3. Half the chord is r2−d2=25−9=4\sqrt{r^2-d^2}=\sqrt{25-9}=4, so the chord is 88. The value 1010 would be the diameter, which occurs only if the line passes through the centre.
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Original question written in the JEE Main 2021 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake