Conic Sections: Parabolas and Circles

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is defined as the set of all points equidistant from a fixed point called the focus and a line called the directrix.

Front

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

Back

The standard form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the focus of a parabola?

Back

The focus is a fixed point located inside the parabola, which is used to define the curve.

Front

What is the directrix of a parabola?

Back

The directrix is a line that is perpendicular to the axis of symmetry of the parabola and is used in conjunction with the focus to define the parabola.

Front

How does the value of 'a' affect the shape of a parabola?

Back

The value of 'a' determines the width and direction of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. Larger absolute values of 'a' make the parabola narrower.

Front

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

Back

The equation is (x - h)² + (y - k)² = r².

Front

What is the center of a circle?

Back

The center of a circle is the fixed point from which all points on the circle are equidistant.

Front

What is the radius of a circle?

Back

The radius is the distance from the center of the circle to any point on the circle.

Front

What is the relationship between the focus and directrix of a parabola?

Back

A parabola is defined as the set of all points that are equidistant from the focus and the directrix.

Front

What happens to the parabola when the x-part is squared?

Back

When the x-part is squared, the parabola opens either upwards or downwards, depending on the sign of the coefficient.