x² + y² - 3x + 8y = -4
You asked:
Investigate the equation: \({x}^{2} + {y}^{2} - 3 x + 8 y = -4\).
MathBot Answer:
The graph of the equation \({x}^{2} + {y}^{2} - 3 x + 8 y = -4\) is a circle.
The coordinates of its center are \(\left(\frac{3}{2}, -4\right)\).
Its radius is \(\frac{\sqrt{57}}{2}\).
The cirlce has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{3}{2} + \frac{\sqrt{57} \cos{\left(\theta \right)}}{2}\\y\left(\theta\right) &= -4 + \frac{\sqrt{57} \sin{\left(\theta \right)}}{2}\end{aligned}\]