4(x+3y)= 100(x^2+y^2)
You asked:
Investigate the equation: \(4 \cdot \left(x + 3 y\right) = 100 \cdot \left({x}^{2} + {y}^{2}\right)\).
MathBot Answer:
The graph of the equation \(4 \cdot \left(x + 3 y\right) = 100 \cdot \left({x}^{2} + {y}^{2}\right)\) is a circle.
The coordinates of its center are \(\left(\frac{1}{50}, \frac{3}{50}\right)\).
Its radius is \(\frac{\sqrt{10}}{50}\).
The cirlce has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{1}{50} + \frac{\sqrt{10} \cos{\left(\theta \right)}}{50}\\y\left(\theta\right) &= \frac{3}{50} + \frac{\sqrt{10} \sin{\left(\theta \right)}}{50}\end{aligned}\]