5$y^{2}$ - 7$y$ = 5$x^{2}$ - 37$x$

asked by guest
on Jan 17, 2025 at 10:27 pm



You asked:

Investigate the equation: \(5 {y}^{2} - 7 y = 5 {x}^{2} - 37 x\).

MathBot Answer:

The graph of the equation \(5 {y}^{2} - 7 y = 5 {x}^{2} - 37 x\) is a hyperbola.

The coordinates of its foci are: \(\left(\frac{37}{10} + \frac{2 \sqrt{165}}{5}, \frac{7}{10}\right)\) and \(\left(\frac{37}{10} - \frac{2 \sqrt{165}}{5}, \frac{7}{10}\right)\).

The coordinates of its vertices are: \(\left(\frac{\sqrt{330}}{5} + \frac{37}{10}, \frac{7}{10}\right)\) and \(\left(\frac{37}{10} - \frac{\sqrt{330}}{5}, \frac{7}{10}\right)\).

The asymptotes have equations: \(10 \sqrt{330} x + 10 \sqrt{330} y - 44 \sqrt{330} = 0\) and \(10 \sqrt{330} x - 10 \sqrt{330} y - 30 \sqrt{330} = 0\).

+ Submit Question