Advertisements
Advertisements
Question
The equations of the lines joining the vertex of the parabola y2 = 6x to the points on it which have abscissa 24 are ______.
Options
y ± 2x = 0
2y ± x = 0
x ± 2y = 0
2x ± y = 0
Solution
The equations of the lines joining the vertex of the parabola y2 = 6x to the points on it which have abscissa 24 are 2y ± x = 0.
Explanation:
Let P and Q be points on the parabola y2 = 6x and OP
OQ be the lines joining the vertex O to the points P
And Q whose abscissa are 24.
Thus y2 = 6 × 24 = 144
or y = ± 12.
Therefore the coordinates of the points P and Q are (24, 12) and (24, –12) respectively.
Hence the lines are y = `+- 12/24 x 2y x`.
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.
y2 = – 8x
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 (–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.
An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
Find the equation of the parabola whose:
focus is (1, 1) and the directrix is x + y + 1 = 0
Find the equation of the parabola whose:
focus is (0, 0) and the directrix 2x − y − 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 (0, −3) and the vertex is at (−1, −3)
Find the equation of a parabola with vertex at the origin and the directrix, y = 2.
Find the equations of the lines joining the vertex of the parabola y2 = 6x to the point on it which have abscissa 24.
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 equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0.
The equation of the parabola whose vertex is (a, 0) and the directrix has the equation x + y = 3a, is
The line 2x − y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The mid-point of PQ 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 equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is
The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is ______.
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.
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.
If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is ______.
