Conics Test

Front

What is the standard equation of a circle?

Back

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

Front

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

Back

The general form is y = ax² + bx + c, where a > 0.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, which is equidistant from the directrix.

Front

How do you identify a circle from its equation?

Back

A circle's equation is in the form (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

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, and the distance from the center to any point on the circle is constant.

Front

What is the standard form of a hyperbola?

Back

The standard form of a hyperbola is (x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/a² - (x - h)²/b² = 1.

Front

What are the characteristics of a parabola?

Back

A parabola has a vertex, focus, directrix, and axis of symmetry. It can open upwards, downwards, left, or right.

Front

What is the equation of a vertical ellipse?

Back

The standard equation of a vertical ellipse is (x - h)²/b² + (y - k)²/a² = 1, where a > b.

Front

What is the equation of a horizontal ellipse?

Back

The standard equation of a horizontal ellipse is (x - h)²/a² + (y - k)²/b² = 1, where a > b.

Front

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

Back

The radius can be found from the equation (x - h)² + (y - k)² = r² by taking the square root of r².