16x^(2)+80x+16y^(2)-112y+247=0
You asked:
Investigate the equation: \(16 {x}^{2} + 80 x + 16 {y}^{2} - 112 y + 247 = 0\).
MathBot Answer:
The graph of the equation \(16 {x}^{2} + 80 x + 16 {y}^{2} - 112 y + 247 = 0\) is a circle.
The coordinates of its center are \(\left(- \frac{5}{2}, \frac{7}{2}\right)\).
Its radius is \(\frac{7}{4}\).
The cirlce has parameterization: \[\begin{aligned}x\left(\theta\right) &= - \frac{5}{2} + \frac{7 \cos{\left(\theta \right)}}{4}\\y\left(\theta\right) &= \frac{7}{2} + \frac{7 \sin{\left(\theta \right)}}{4}\end{aligned}\]