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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

Front

What are the coordinates of the vertices of an ellipse?

Back

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

Tags

CCSS.HSG.GPE.A.1

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).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

(x - h)² + (y - k)² = r².

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

Radius = Diameter / 2.

Tags

CCSS.7.G.B.4

Front

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

Back

Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Tags

CCSS.HSG.GPE.A.1

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.