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Question

# Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.$100x^2+100y^2-100x+400y+409=0$

Solution

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Given:

$100x^2+100y^2-100x+400y+409=0$

We need to determine whether the given equation corresponds to a circle, parabola, ellipse, or hyperbola.

• If either the $x$-variable or the $y$-variable isn't squared, then the equation belongs to a parabola.
• If either $x^2$ or $y^2$ (but not both) contains a minus sign in front, then the equation belongs to a hyperbola.
• If the coefficients of $x^2$ and $y^2$ have the same sign but different values for the coefficients, then the equation belongs to an ellipse.
• If the coefficients of $x^2$ and $y^2$ have the same coefficients, then the equation belongs to a circle.

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