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QJEEM24Mad469: JEE Main 2024 Mathematics - Class 11 JEEM24Mad469 Solution: If one of the diameters of the circle is a chord of another…

If one of the diameters of the circle x2+y2−10x+4y+13=0x^2+y^2-10 x+4 y+13=0 is a chord of another circle C\mathrm{C} , whose center is the point of intersection of the lines 2x+3y=122 x+3 y=12 and 3x−2y=53 x-2 y=5 , then the radius of the circle C\mathrm{C} is :

Multiple Choice Options

  • A 4
  • B 3 2\sqrt2
  • C 6
  • D 20\sqrt{20}

Step-by-Step Verified Solution

JEE Main 2024 (Online) 31st January Morning Shift Mathematics - Circle Question 21 English Explanation

amp;2x+3y=12amp;3x−2y=5\begin{aligned}& 2 x+3 y=12 \\& 3 x-2 y=5\end{aligned}

amp;13x=39amp;x=3,y=2\begin{aligned}& 13 x=39 \\& x=3, y=2\end{aligned}

Center of given circle is (5,−2)(5,-2)

Radius 25+4−13=4\sqrt{25+4-13}=4

amp;∴CM=4+16=52amp;∴CP=16+20=6\begin{aligned}& \therefore \mathrm{CM}=\sqrt{4+16}=5 \sqrt{2} \\& \therefore \mathrm{CP}=\sqrt{16+20}=6\end{aligned}

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