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JEE Main 201322 AprilOnline
Exam
JEE Main
Year
2013
Date
22 April
Mode
Online
Subject
Mathematics
Chapter
Circle

JEE Main 2013 · 22 April · Online · Mathematics · Circle

If a circle C passing through (4,0) touches the circle x^2+y^2+4...

If a circle C\mathrm{C} passing through (4,0)(4,0) touches the circle x2+y2+4x−6y−12=0x^2+y^2+4 x-6 y-12=0 externally at a point (1,−1)(1,-1), then the radius of the circle C\mathrm{C} is :If a circle C passing through (4,0) touches the circle x^2+y^2+4 x-6 y-12=0 externally at a point (1,-1) , then theIf a circle C passing through (4,0) touches the circle x^2+y^2+4 x-6 y-12=0 externally at a point (1,-1) , then the

Options

  1. A5
  2. B252 \sqrt{5}
  3. C4
  4. D57\sqrt{57}

Correct answer

A. 5

Step-by-step solution

Let A be the centre of given circle and B\mathrm{B} be the centre of circle C. If a circle C passing through (4,0) touches the circle x^2+y^2+4 x-6 y-12=0 externally at a point (1,-1) , then the
x2+y2+4x−6y−12=0∴A=(−2,3) and B=(g,f)\begin{aligned}& x²+y²+4 x-6 y-12=0 \\ & \therefore A=(-2,3) \text{ and }B=(g, f) \end{aligned}Now, from the figure, we have−2+g2=\frac{-2+g}{2}=1 \text{ and} \frac{3+f}{2}=-1(Bymidpointformula)⇒g=41 (By mid point formula) \Rightarrow g=4\text{and }f=-5 Now, required radius =\mathrm{OB}=\sqrt{9+16}=\sqrt{25}=$5
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