Write the equation of the unit circle concentric with x^2 + y^2 -… - Vidyadip

Question

Write the equation of the unit circle concentric with $x^2 + y^2 - 8x + 4y - 8 = 0.$

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Answer

$x^2 + y^2 - Bx + 4y - 8 = 0$
$x^2 - Bx + (4)^2 - (4)^2 + y^2 + 4y + (2)^2 - (2)^2 - 8 = 0$
$(x - 4)^2 + (y + 2)^2 - 16 - 4 - 8 = 0$
$(x - 4) + (y + 2) - 28 = 0$
$(x - 4)^2 + (y + 2)^2 = 28 .......... (1)$
Concentric unit circle to equation $(1)$ is
$(x - 4)^2 + (y + 2)^2 = 1$
$x^2 - Bx + y^2 + 4y + 19 = 0$

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