The general second-degree equation for a conic section is:
\[ Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 \]
The type of conic is determined by the discriminant (B² - 4AC):
A conic section is a curve obtained by intersecting a cone with a plane. The different types of conic sections (ellipse, parabola, hyperbola, and circle) are determined by the angle at which the plane intersects the cone and the shape of the resulting curve. These curves have various applications in physics, engineering, astronomy, and other fields.
Let's assume the following values:
Using the formula:
Discriminant (\(B² - 4AC\)):
\[ 2^2 - 4 \times 1 \times 1 = 4 - 4 = 0 \]
Since the discriminant is 0, the conic is a parabola.
Let's assume the following values:
Using the formula:
Discriminant (\(B² - 4AC\)):
\[ 0^2 - 4 \times 3 \times 3 = 0 - 36 = -36 \]
Since the discriminant is less than 0 and \(A = C\) and \(B = 0\), the conic is a circle.
