Question:
Determine the form of the conic section described by the equation \( x^2 + y^2 + 2xy - 8x + 8y = 0 \)
Determine the form of the conic section described by the equation \( x^2 + y^2 + 2xy - 8x + 8y = 0 \)
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When the \( xy \)-term is present in a second-degree equation, the conic section is typically a hyperbola or a parabola, depending on the other terms.
Updated On: Apr 1, 2025
- Circle
- Parabola
- Hyperbola
- A pair of straight lines
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The Correct Option is B
Solution and Explanation
The given equation is of the form:
\[
x^2 + y^2 + 2xy - 8x + 8y = 0
\]
This is a second-degree equation in two variables. The presence of the \( xy \) term indicates that it is a parabola. Thus, the correct answer is Parabola.
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