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Find the equation of a parabola whose vertex is at (0,0) and focus at (-3/2,0). Also, find its focal length and where the parabola is opened.
Find the equation of a parabola whose vertex is at (0,0) and focus at (3,0). Also, find its focal length and where the parabola is opened.
Find the equation of a parabola whose vertex is at (0,0) and focus at (0,4). Also, find its focal length and where the parabola is opened.
Find the equation of a parabola whose vertex is at (3,2) and focus at (6,2). Also, find its focal length and where the parabola is opened.
Find the equation of a parabola whose vertex is at (5,3) and focus at (5,6). Also, find its focal length and where the parabola is opened.
Find the equation of the parabola whose focus is at (4,0) and its directrix is x = -4.
Find the equation of the parabola whose vertex is at the origin, passes through the point (5,2), and symmetric about the y-axis.
Find the equation of a parabola whose length of latus rectum is 16, axis parallel to the x-axis, and passing through (3,2) and (3,-2).
For the parabola 3y2 = 8x, find:
- the coordinates of the vertex
- the coordinates of the focus
- equation axis of the parabola
- equation of directrix
- length of latus rectum
- the coordinates of the ends of the latus rectum
For the parabola x2 = -8y, find:
- the coordinates of the vertex
- the coordinates of the focus
- equation axis of the parabola
- equation of directrix
- length of latus rectum
- the coordinates of the ends of the latus rectum
For the parabola (y - 2)2 = 2(x + 3), find:
- the coordinates of the vertex
- the coordinates of the focus
- equation axis of the parabola
- equation of directrix
- length of latus rectum
- the coordinates of the ends of the latus rectum
For the parabola x2 - 4x - 3y + 13 = 0 find:
- the coordinates of the vertex
- the coordinates of the focus
- equation axis of the parabola
- equation of directrix
- length of latus rectum
- the coordinates of the ends of the latus rectum
Find the focal distance of a point P(2,4) for the parabola y2 = 8x.
Find the focal distance of a point P(4,1) for the parabola x2 = 16y.
At what points on the parabola y2 = 36x is the ordinate two times that of its abscissa?
Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.
Find the locus of the mid-points of the chords of a parabola y2 = 4ax, drawn from focus. Prove that the locus is a parabola.
A double ordinate of the curve y2 = 4ax is of length 8a. Prove that the lines joining the vertex to its ends are at right angles.
Find the parametric equation of the parabola y2 = 10x.
Find the parametric equation of the parabola x2 = -16y.