The equation of the axis of the parabola x² = 24y is:
Find the equation of the parabola that has its vertex at the origin, passes through the point (5, 2), and is symmetric about the y-axis.
Find the equation of the parabola that has its vertex at the origin, has directrix y = −3, and has its axis along the x-axis or y-axis.
For the parabola x² = 4y, the equations of the directrix and the axis are:
The focus and vertex of the parabola y² = 12x are:
Find the value of a for which the parabola y² = 4ax passes through the point (−3, 4).
The length of the latus rectum of the parabola x² = 5y is:
The length and the equation of the latus rectum of the parabola x² = 10y are:
The focus of the parabola y² − 8x − 6y − 23 = 0 is:
The equation of the directrix of the parabola x² = −16y is:
The slope of the tangent to the parabola y² = 4ax at the point (a, 2a) is:
The vertex of the parabola y² − 8x − 6y − 23 = 0 is:
The general second-degree equation ax² + 2hxy + by² + cx + dy + e = 0 represents a parabola if:
The equation and the length of the latus rectum of the parabola y² − 8x − 6y − 23 = 0 are:
If the focus is F′(0, −a) and the directrix is the line y = a, then the equation of the parabola is:
The equation of the directrix of the parabola y² − 6y − 6x + 21 = 0 is:
The equation of the parabola with vertex (3, 2) and the endpoints of its focal chord at (5, 6) and (5, −2) is:
The equation of the parabola with focus (−5, 3) and directrix y = 7 is:
The equation of the directrix of the parabola y² − 6y − 6x + 21 = 0 is:
The coordinates of the vertex and focus of the parabola x² + 4x + 2y = 1 are:
