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Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
focus is (1, 1) and the directrix is x + y + 1 = 0
focus is (0, 0) and the directrix is 2x - y – 1 = 0
focus is (2, 3) and the directrix is x - 4y + 1 = 0
Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0. Also, find the length of its latus - rectum.
Find the equation of the parabola, if
the focus is at (- 6, 6) and the vertex is at (- 2, 2)
the focus is at (0, - 3) and the vertex is at (0, 0)
the focus is at (0, - 3) and the vertex is at (- 1, - 3)
the focus is at (a, 0) and the vertex is at (a’, 0)
the focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x – y = 3
Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas
y2 = 8x
4x2 = y
y2 - 4y - 3x + 1 = 0
y2 - 4y + 4x = 0
y2 + 4x + 4y - 3 = 0
y2 = 8x + 8y
4(y - 1)2 = - 7(x - 3)
y2 = 5x - 4y – 9
x2 + y = 6x – 14
For the parabola, y2 = 4px find the extremities of a double ordinate of length 8p. Prove that the lines from the vertex to its extremities are at right angles.
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 coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3, 3) and directrix is 3x – 4y = 2. Find also the length of the latus - rectum.
At what point of the parabola x2 = 9y is the abscissa three times that of ordinate?
Find the equation of a parabola with vertex at the origin, the axis along the x - axis and passing through (2, 3).
Find the equation of a parabola with vertex at the origin and the directrix, y = 2.
Find the equation of the parabola whose focus is (5, 2) and having a vertex at (3, 2).
The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30m and the shortest wire being 6m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
Find the equations of the lines joining the vertex of the parabola y2 = 6x to the point on it which have abscissa 24.
Find the coordinates of points on the parabola y2 = 8x whose focal distance is 4.
Find the length of the line segment joining the vertex of the parabola y2 = 4ax and a point on the parabola where the line - segment makes an angle θ to the x - axis.
If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
If the line y = mx + 1 is tangent to the parabola y2 = 4x, then find the value of m.
Write the axis of symmetry of the parabola y2 = x.
write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0
Write the equation of the directrix of the parabola x2 – 4x – 8y + 12 = 0
Write the equation of the parabola with focus (0, 0) and directrix x + y – 4 = 0.
Write the length of the chord of the parabola y2 = 4ax which passes through the vertex and is inclined to the axis at π/4.
If b and c are lengths of the segments of any focal chord of the parabola y2 = 4ax, then write the length of its latus - rectum.
PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ.
Write the coordinates of the vertex of the parabola whose focus is at (- 2, 1) and directrix is the line x + y – 3 = 0.
If the coordinates of the vertex and focus of a parabola are (- 1, 1) and (2 , 3) respectively then write the equation of its directrix.
If the parabola y2 = 4ax passes through the point (3, 2), then find the length of its latus - rectum.
Write the equation of the parabola whose vertex is at (- 3, 0) and the directrix is x + 5 = 0.
The coordinates of the focus of the parabola y2 – x – 2y + 2 = 0
The vertex of the parabola (y + a)2 = 8a(x – a) is
If the focus of a parabola is (- 2, 1) and the directrix has the equation x + y = 3, then its vertex is
The equation of the parabola whose vertex is (a, 0) and the directrix has the equation x + y = 3a, is
The parametric equations of a parabola are x = t2 + 1, y = 2t + 1. The Cartesian equation of its directrix is
If the coordinates of the vertex and the focus of a parabola are (- 1, 1) and (2, 3) respectively, then the equation of its directrix is
The locus of the points of trisection of the double ordinates of a parabola is a
The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is
If V and S are respectively the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0, then SV =
The directrix of the parabola x2 – 4x – 8y + 12 = 0 is
The equation of the parabola with focus (0, 0) and directrix x + y = 4 is
The line 2x – y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The mid - point of PQ is
In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at is
The equation 16x2 + y2 + 8xy – 74x – 78y + 212 = 0 represents
The length of the latus - rectum of the parabola y2 + 8x – 2y + 17 = 0 is
The vertex of the parabola x2 + 8x + 12y + 4 = 0 is
The vertex of the parabola (y – 2)2 = 16(x – 1) is
The length of the latus - rectum of the parabola 4y2 + 2x – 20y + 17 = 0 is
The length of the latus - rectum of the parabola x2 – 4x – 8y + 12 = 0 is
The focus of the parabola y = 2x2 + x is
Which of the following points lie on the parabola x2 = 4ay?
The equation of the parabola whose focus is (1, - 1) and the directrix is x + y + 7 = 0 is
