🟣Conic Sections Review

Front

What is the standard form of the equation of a parabola with focus (0, 4) and directrix y = -4?

Back

y = (1/16)x²

Front

What are the foci of the shifted ellipse with foci (√3 - 3, 1) and (-√3 - 3, 1)?

Back

(√3 - 3, 1) and (-√3 - 3, 1)

Front

Find the vertex, focus, and directrix of the parabola given by the equation y = (1/4)(x - 3)² + 2.

Back

Vertex: (3, 2), Focus: (5, 2), Directrix: x = 1

Front

What is the equation of a circle with center (-1, -1) and radius 3?

Back

(x + 1)² + (y + 1)² = 9

Front

Find the equation of the hyperbola represented by the graph with vertices at (1, -2) and (1, 2).

Back

(x - 1)²/16 - (y + 2)²/4 = 1

Front

What is the definition of a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane.

Front

What is the standard form of the equation of a circle?

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What is the standard form of the equation of an ellipse?

Back

(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 is the standard form of the equation of a hyperbola?

Back

(x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center.

Front

What is the focus of a parabola defined by the equation y = (1/4p)(x - h)² + k?

Back

Focus: (h, k + p)