Pre-Calc: Conics

Front

What is the standard form of a parabola that opens upwards?

Back

The standard form is (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the equation of a circle with center (h, k) and radius r?

Back

The equation is (x - h)² + (y - k)² = r².

Front

Identify the conic section represented by the equation: (x - 2)² + (y + 3)² = 16.

Back

This is a circle with center (2, -3) and radius 4.

Front

What is the definition of a directrix in relation to a parabola?

Back

The directrix is a line perpendicular to the axis of symmetry of the parabola, located at a distance p from the vertex, opposite to the focus.

Front

What is the general form of a conic section?

Back

The general form is Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Front

What distinguishes an ellipse from a hyperbola?

Back

An ellipse has a positive discriminant (B² - 4AC < 0), while a hyperbola has a negative discriminant (B² - 4AC > 0).

Front

What is the focus of a parabola?

Back

The focus is a point located p units from the vertex along the axis of symmetry, where all points on the parabola are equidistant from the focus and the directrix.

Front

Write the equation of a parabola that opens to the right with vertex at (0, 0).

Back

The equation is y² = 4px, where p is the distance from the vertex to the focus.

Front

What is the center of the ellipse given by the equation: 9(x - 1)² + 4(y + 2)² = 36?

Back

The center is (1, -2).

Front

How do you find the radius of a circle from its equation?

Back

The radius is the square root of the constant term on the right side of the equation in the form (x - h)² + (y - k)² = r².