Conic Sections Review (Circles, Ellipses, Hyperbolas)

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The main types are circles, ellipses, parabolas, and hyperbolas.

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

Identify the conic section represented by the equation: x² + y² - 10x - 4y - 21 = 0.

Back

Circle.

Front

What is the center of the circle given by the equation (x - 3)² + (y + 5)² = 16?

Back

(3, -5).

Front

What is the value of the radius for the circle (x - 5)² + (y - 10)² = 25?

Back

5 (since radius r = √25).

Front

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

Back

The general form is (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center, and a and b are the semi-major and semi-minor axes.

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the lengths of the semi-major and semi-minor axes are equal.

Front

What is the standard form of a hyperbola?

Back

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

Front

What does the variable 'a' represent in the equation of a hyperbola?

Back

The distance from the center to the vertices along the transverse axis.

Front

What is the direction of a parabola represented by the equation y = ax² + bx + c?

Back

If a > 0, it opens upwards; if a < 0, it opens downwards.