Identifying conic sections

Front

What are the four types of conic sections?

Back

The four types of conic sections are: 1) Circle, 2) Ellipse, 3) Parabola, 4) Hyperbola.

Front

What is the general form of a conic section equation?

Back

The general form of a conic section equation is Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.

Front

How can you identify a parabola from its equation?

Back

A parabola can be identified by the presence of only one squared term in its equation, such as y = ax² + bx + c or x = ay² + by + c.

Front

What is the standard form of an ellipse equation?

Back

The standard form of an ellipse equation is (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

Front

What distinguishes a hyperbola from other conic sections?

Back

A hyperbola is distinguished by having two squared terms with opposite signs in its equation, such as (x-h)²/a² - (y-k)²/b² = 1.

Front

What is the significance of the discriminant in conic sections?

Back

The discriminant (B² - 4AC) helps determine the type of conic section represented by the equation: if > 0, it's a hyperbola; if = 0, it's a parabola; if < 0, it's an ellipse or circle.

Front

What is the equation of a circle in standard form?

Back

The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

How do you convert the general form of a conic section to standard form?

Back

To convert to standard form, complete the square for the x and y terms, and rearrange the equation.

Front

What is the relationship between the axes of symmetry and conic sections?

Back

Conic sections have axes of symmetry: circles and ellipses have two axes, parabolas have one, and hyperbolas have two distinct axes.

Front

What is the focal property of a parabola?

Back

The focal property of a parabola states that any point on the parabola is equidistant from the focus and the directrix.