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JEE Main 20248 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2024 · 8 April · Evening Shift · Mathematics · Straight Lines

If the image of the point (-4,5) in the line x+2 y=2 lies on the...

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 r\mathrm{r} is equal to:

Options

  1. A2
  2. B3
  3. C1
  4. D4

Correct answer

A. 2

Step-by-step solution

Image of point (−4,5)(-4,5) x−x1a=y−y1b=−2\frac{x-x_1}{a}=\frac{y-y_1}{b}=-2\left(\frac{a x_1+b y_1+c}{a^2+b^2}\right)Line:Line:x+2 y-2=0 \frac{x+4}{1}=\frac{y-5}{2}=-2\left(\frac{-4+10-2}{1^2+2^2}\right)=−85=\frac{-8}{5} x=−4−85=−285x=-4-\frac{8}{5}=-\frac{28}{5} y=−165+5=95y=-\frac{16}{5}+5=\frac{9}{5} Point lies on circle (x+4)2+(y−3)2=r2(x+4)^2+(y-3)^2=r^2 6425+(95−3)2=r210025=r2,r=2\begin{aligned} & \frac{64}{25}+\left(\frac{9}{5}-3\right)^2=r^2 \\ & \frac{100}{25}=r^2, r=2\end{aligned}
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