Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. $5x^2 - 4xy + 5y^2 - 16 = 0$ (a) Identify the resulting rotated conic. $\bigcirc$ parabola $\bigcirc$ ellipse $\bigcirc$ hyperbola (b) Give its equation in the new coordinate system. (Use $x_p$ and $y_p$ as the new coordinates.) $3x_p^2 + 7y_p^2 - 16 = 0$
Added by Martin R.
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We can identify the coefficients as follows: A = 5, B = -4, and C = 5. Show more…
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