Advertisements
Advertisements
प्रश्न
The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is
विकल्प
x + 2y = 4
x − y = 3 1
2x + y = 5
x + 3y = 8
उत्तर
x + 2y = 4
Given:
The vertex and the focus of a parabola are (1, 4) and (2, 6), respectively.
∴ Slope of the axis of the parabola = \[\frac{6 - 4}{2 - 1} = 2\]
Slope of the directrix = \[\frac{- 1}{2}\]
Let the directrix intersect the axis at K (r, s).
\[\frac{r + 2}{2} = 1, \frac{s + 6}{2} = 4\]
\[ \Rightarrow r = 0, s = 2\]
Equation of the directrix:
\[\left( y - 2 \right) = \frac{- 1}{2}\left( x - 0 \right)\]
\[\Rightarrow\] x + 2y = 4
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 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 (2, 3) and axis is along x-axis
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.
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?
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 (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, −3) and the vertex is at (−1, −3)
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 and the directrix, y = 2.
PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ.
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
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 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 (1, −1) and the directrix is x + y + 7 = 0 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 coordinates of a point on the parabola y2 = 8x whose focal distance is 4.
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 following parabolas:
Focus at (–1, –2), directrix x – 2y + 3 = 0
The line lx + my + n = 0 will touch the parabola y2 = 4ax if ln = am2.
The equation of the parabola having focus at (–1, –2) and the directrix x – 2y + 3 = 0 is ______.
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 ______.
The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity `1/2` is ______.
