Given that we need to find the equation of the circle which is concentric with x2 + y2 - 6x + 12y + 15 = 0 and double its area.
We know that concentric circles will have the same centre.
Let us assume the concentric circle be x2 + y2 - 6x + 12y + c = 0. .....(ii)
We know that for a circle x2 + y2 + 2ax + 2by + c = 0 - - (1)
⇒ Centre = (- a, - b)
⇒ Radius =
Let us assume the radius of the first circle is r1.
Given that the concentric circle’s area is double the first circle’s area.
Let us assume the radius of the concentric circle be r2.
We know that the area of the circle is πr2
⇒ Area of concentric circle = 2 × area of the first circle
⇒ r22 = 60
⇒ r2 = √60
Comparing with (ii) with (1), we get
⇒ 9 + 36 - c = 60
⇒ c = - 15
Substituting c value in (ii), we get
⇒ x2 + y2 - 6x + 12y - 15 = 0
∴ The equation of the concentric circle is x2 + y2 - 6x + 12y - 15 = 0.
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