Advertisements
Advertisements
प्रश्न
Write the equation of the directrix of the parabola x2 − 4x − 8y + 12 = 0.
Advertisements
उत्तर
Given:
x2 − 4x − 8y + 12 = 0
\[ \Rightarrow \left( x - 2 \right)^2 = 8\left( y - 1 \right) \left( 1 \right)\]
Let Y = y−1, \[X = x - 2\]
∴ From (1), we have:
\[X^2 = 8Y\]
Comparing with \[x^2 = 4ay\]
\[a = 2\]
Directrix = Y = −a
⇒ y − 1 = −a
⇒y = −a + 1
= −2 + 1
= −1
Therefore, the required equation of the directrix is \[y = - 1\]
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.
y2 = – 8x
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 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 (1, 1) and the directrix is x + y + 1 = 0
Find the equation of the parabola if
the focus is at (0, −3) and the vertex is at (0, 0)
Find the equation of the parabola if the focus is at (a, 0) and the vertex is at (a', 0)
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.
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.
Find the equation of the parabola whose focus is (5, 2) and having vertex at (3, 2).
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.
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 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 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.
If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
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 ______.
The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity `1/2` is ______.
