Verified Solution • 2025–26 Session moderate

QJEEM24Madca0: JEE Main 2024 Mathematics - Class 11 JEEM24Madca0 Solution: If the image of the point in the line lies on the circle , then …

If the image of the point (−4,5)(-4,5) in the line x+2y=2x+2 y=2 lies on the circle (x+4)2+(y−3)2=r2(x+4)^2+(y-3)^2=r^2 , then rr is equal to:

Multiple Choice Options

  • A 2
  • B 3
  • C 4
  • D 1

Step-by-Step Verified Solution

amp;x+41=y−52=−2(4)5amp;⇒x=−4−85=−285,y=5−165=95amp;∴ Image is (−285,95)\begin{aligned}& \frac{x+4}{1}=\frac{y-5}{2}=\frac{-2(4)}{5} \\& \Rightarrow \quad x=-4-\frac{8}{5}=-\frac{28}{5}, y=5-\frac{16}{5}=\frac{9}{5} \\& \therefore \quad \text { Image is }\left(\frac{-28}{5}, \frac{9}{5}\right)\end{aligned}

Image lies on circle (x+4)2+(y−3)2=r2(x+4)^2+(y-3)^2=r^2

amp;(−285+4)2+(95−3)2=r2amp;⇒6425+3625=r2amp;⇒r=2\begin{aligned}& \left(\frac{-28}{5}+4\right)^2+\left(\frac{9}{5}-3\right)^2=r^2 \\& \Rightarrow \frac{64}{25}+\frac{36}{25}=r^2 \\& \Rightarrow r=2\end{aligned}

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