Advertisements
Advertisements
प्रश्न
Find the equation of the following parabolas:
Vertex at (0, 4), focus at (0, 2)
उत्तर
Given that vertex at (0, 4) and focus at (0, 2).
So, the equation of directrix is y – 6 = 0
According to the definition of the parabola
PF = PM.
`sqrt((x - 0)^2 + (y - 2)^2) = |y - 6|`
⇒ `sqrt(x^2 + y^2 + 4 - 4y) = |y - 6|`
Squaring both the sides, we get
x2 + y2 + 4 – 4y = y2 + 36 – 12y
⇒ x2 + 4 – 4y = 36 – 12y
⇒ x2 + 8y – 32 = 0
⇒ x2 = 32 – 8y
Hence, the required equation is x2 = 32 – 8y.
APPEARS IN
संबंधित प्रश्न
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 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 (6, 0); directrix x = –6
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), passing through (5, 2) and symmetric with respect to y-axis.
Find the equation of the parabola whose:
focus is (2, 3) and the directrix x − 4y + 3 = 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)
Find the equation of the parabola if the focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x − y = 3.
Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).
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 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.
Write the equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0.
The parametric equations of a parabola are x = t2 + 1, y = 2t + 1. The cartesian equation of its directrix is
The equation 16x2 + y2 + 8xy − 74x − 78y + 212 = 0 represents
If V and S are respectively the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0, then SV =
The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is ______.
Find the coordinates of a point 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.
Find the equation of the following parabolas:
Directrix x = 0, focus at (6, 0)
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 line lx + my + n = 0 will touch the parabola y2 = 4ax if ln = am2.
If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation 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 ______.
