Question

If $z\bar{z} : + (3 - 4i) z + (3 + 4i) \bar{z} =0$ represent a circle, the area of the circle in square units is

• A. $5\pi$
• B. $10 \pi$
• C. $25 \,\pi^2$
• D. $25\pi$

Answer 1

Answer: (D)

Given $z\bar{z} + (3 - 4i) z + (3 + 4i)\bar{z} = 0$
Let $z = x + iy $
$\therefore z \bar{z} = x^2 + y^2$
$\Rightarrow x^2 + y^2 + (3 - 4i) (x + iy) + (3 + 4i) (x - iy) = 0$
$\Rightarrow x^2 +y^2 + 6x + 8y = 0$
$\Rightarrow (x^2 + 6x) + (y^2 + 8y) = 0$
$\Rightarrow (x + 3)^2 + (y + 4)^2 = 3^2 + 4^2$
$\Rightarrow [x - ( - 3)]^2 + [y - (-4 ) ] ^2 = 5^2$
$( \because R =$ radius $= 5)$
So area of circle be $\pi R^2 = 25\pi$