Flashcard #6 Review/Conic Sections

Front

If the plane intersects the cone parallel to the x-axis, the curve formed is a/an ____________.

Back

Circle

Front

Which way does the parabola (y - 4)² = -8(x + 1) open?

Back

Left

Front

What is the center of the hyperbola with the equation (x + 4)²/16 - (y - 0)²/9 = 1?

Back

(-4, 0)

Front

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

Back

y = a(x - h)² + k, where (h, k) is the vertex.

Front

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

Back

(x - h)² + (y - k)² = r²

Front

What type of conic section is formed when the plane intersects the cone at an angle?

Back

Hyperbola

Front

What is the equation of an ellipse centered at the origin with semi-major axis a and semi-minor axis b?

Back

(x²/a²) + (y²/b²) = 1

Front

Identify the conic section: x² - y² = 1.

Back

Hyperbola

Front

What is the vertex form of a parabola?

Back

y = a(x - h)² + k

Front

What is the distance between the foci of a hyperbola given by the equation (x²/a²) - (y²/b²) = 1?

Back

2c, where c = √(a² + b²)