Write the equation of the unit circle concentric with x2 + y2 – 8x + 4y – 8 = 0.
Given that we need to find the equation of the circle which is concentric with x2 + y2 - 8x + 4y - 8 = 0 and having a unit radius.
We know that concentric circles will have the same centre.
Let us assume the concentric circle be x2 + y2 - 8x + 4y + c = 0. ...... (ii)
We know that for a circle x2 + y2 + 2ax + 2by + c = 0 ...... (1)
⇒ Centre = (- a, - b)
⇒ Radius =
We know that unit circle has radius 1.
⇒
⇒ 1 = 16 + 4 - c
⇒ c = 19
∴ The equation of the concentric circle is x2 + y2 - 8x + 4y + 19 = 0.