Conics - Precalculus

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

How do you find the center of a circle given its equation?

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

What are the coordinates of the vertices of an ellipse?

Back

The vertices are the points where the ellipse intersects its major axis.

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the two foci coincide.

Front

How do you determine if a hyperbola opens vertically or horizontally?

Back

If the equation is of the form (y - k)²/a² - (x - h)²/b² = 1, it opens vertically; if (x - h)²/a² - (y - k)²/b² = 1, it opens horizontally.

Front

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

(x - h)² + (y - k)² = r².

Front

How do you find the radius of a circle given its diameter?

Back

Radius = Diameter / 2.

Front

What is the general form of the equation of a conic section?

Back

Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Front

What are the foci of an ellipse?

Back

The foci are two fixed points located along the major axis, used to define the ellipse.