What is the radius of a circle x² + y² + 4x + 8y -16 = 0 whose diameters are x + y = -6 and x - y = 2, respectively.

What is the radius of a circle x² + y² + 4x + 8y -16 = 0 whose diameters are x + y = -6 and x - y = 2, respectively?
a) 2 units
b) 6 units
c) 7 units
d) 10 units

Answer: b) 6 units

Solution:

Given,

Equation of circle = $x^2 + y^2 + 4x + 8y - 16 = 0$

Comparing the given equation with general equation of circle, we get,

$2gx = 4x$

$or, g = 2$

$2fy = 8y$

$or, f = 4$

$c =-16$

Using formula to find the radius,

$r = \sqrt{g^2 + f^2 - c}$

$or, r = \sqrt{2^2 + 4^2 - (-16)}$

$or, r = \sqrt{4 + 16 + 16}$

$or, r = \sqrt{36}$

$\therefore r = 6 units$

Hence, the required radius of the circle is 6 units.

Note: Equations of diameters are not necessary to be solved!

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