Question

X^2 + y^2 - 6x + 8y = 144

Answer 1

The diameter of the equation of a circle in the xy-plane as shown is 26 units.

The standard form for finding the equation of a circle is expressed as:

$x^2 + y^2 +2gx + 2fy +C= 0$

For us to get the diameter of the circle, we need to get the radius of the circle first calculated as shown:

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

Given the equation of the circle expressed as $x^2 + y^2 - 6x + 8y = 144$

Compare with the general formula:

2gx = -6x

g = -6/2

g = -3

Similarly;

2fy = 8y

2f = 8

f = 4

C = -144

Substitute into the formula for calculating the radius;

$r=\sqrt{(-3}^2+4^2-(-144)\\r=\sqrt{9+16+144}\\r=\sqrt{169}\\r=13units$

Get the diameter of the circle

d = 2r

d = 2(13)

d = 26 units

Hence the diameter of the equation of a circle in the xy-plane as shown is 26 units.

Learn more here: brainly.com/question/12908710