Advertisements
Advertisements
Question
Find the equation of a parabola with vertex at the origin and the directrix, y = 2.
Solution
Let the equation of the directrix be y = a.
a = 2
Equation of the parabola with directrix y =a is \[x^2 = - 4ay\]
Hence, the required equation of the parabola is \[x^2 = - 8y\]
APPEARS IN
RELATED QUESTIONS
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.
x2 = 6y
Find the equation of the parabola that satisfies the following condition:
Focus (0, –3); directrix y = 3
Find the equation of the parabola that satisfies the following condition:
Vertex (0, 0); focus (3, 0)
Find the equation of the parabola that satisfies the following condition:
Vertex (0, 0) focus (–2, 0)
Find the equation of the parabola that satisfies the following condition:
Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
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 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.
Find the equation of the parabola if
the focus is at (−6, −6) and the vertex is at (−2, 2)
Find the equation of the parabola if the focus is at (0, −3) and the vertex is at (−1, −3)
Find the equation of the parabola if the focus is at (a, 0) and the vertex is at (a', 0)
Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).
Find the equation of the parabola whose focus is (5, 2) and having vertex at (3, 2).
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.
If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
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.
PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ.
The line 2x − y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The mid-point of PQ is
The equation 16x2 + y2 + 8xy − 74x − 78y + 212 = 0 represents
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 equation of the parabola whose focus is (1, −1) and the directrix is x + y + 7 = 0 is
An equilateral triangle is inscribed in the parabola y2 = 4ax whose one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
Find the equation of the following parabolas:
Directrix x = 0, focus at (6, 0)
Find the equation of the following parabolas:
Vertex at (0, 4), focus at (0, 2)
Find the equation of the set of all points whose distance from (0, 4) are `2/3` of their distance from the line y = 9.
The equation of the parabola having focus at (–1, –2) and the directrix x – 2y + 3 = 0 is ______.
If the vertex of the parabola is the point (–3, 0) and the directrix is the line x + 5 = 0, then its equation is ______.
The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity `1/2` is ______.
