(x-1)^2/64 + (y+4)^2/49 = 1

asked by guest
on Jan 26, 2025 at 8:44 pm



You asked:

Investigate the equation: \(\frac{{\left( x - 1 \right)}^{2}}{64} + \frac{{\left( y + 4 \right)}^{2}}{49} = 1\).

MathBot Answer:

\(\frac{{\left( x - 1 \right)}^{2}}{64} + \frac{{\left( y + 4 \right)}^{2}}{49} = 1\) is an equation of an ellipse, and is equivalent to \(\frac{\left(x - 1\right)^{2}}{64} + \frac{\left(y + 4\right)^{2}}{49} = 1\).

It is centered at \(\left(1, -4\right)\).

Its foci are \(\left(1 + \sqrt{15}, -4\right)\) and \(\left(1 - \sqrt{15}, -4\right)\).

Its minor axis has length \(14\) with endpoints \(\left(1, -11\right)\) and \(\left(1, 3\right)\).

Its major axis has length \(16\) with endpoints \(\left(-7, -4\right)\) and \(\left(9, -4\right)\).

The ellipse has parameterization: \[\begin{aligned}x\left(\theta\right) &= 1 + 8 \cos{\left(\theta \right)}\\y\left(\theta\right) &= -4 + 7 \sin{\left(\theta \right)}\end{aligned}\]

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