Question

The radius of the circle passing through $(6,2)$ and equations of two normals for the circle are $x+y=6$ and $x+2y=4$ is

• A. $\sqrt{5}$
• B. $2\sqrt{5}$
• C. $3\sqrt{5}$
• D. $4\sqrt{5}$

Answer 1

The correct option is B $2\sqrt{5}$

• Normals of circle = Diameter
  
• With the help of given equations we can find the center of circle
  

x+y=6 -(1)

x+2y=4 -(2)

• we use elimination method, then 1st equation becomes 2x+2y=12 bymultiply 2
  

and 2nd remains same x+2y=4

after solving these equations we get x=8 and y=-2

so center point of the circle is (8,-2).

and other point is given from which circle is passing i.e (6,2)

• If we find the distance between these two points the we will get the radius of the circle.
  

Therefore, √ ((x2-x1)^2 + (y2-y1)^2)

√( (8–6)^2 + (-2–2)^2)

√( 2^2 + (-4)^2)

√ 4+16

√ 20 = 2√ 5(Ans)