Advertisements
Advertisements
प्रश्न
Write the equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0.
उत्तर
The general equation of the parabola is (y − k)2 = 4a(x − h)
Here, the (h, k) = (−3,0)
Now, the directrix is given by
x = h − a
⇒ −5 = −3 − a [∵ x + 5 = 0 ⇒ x = −5]
⇒ a = 2
Hence, the equation is given by
(y − 0)2 = 4(2)(x + 3)
⇒ y2 = 8 (x + 3)
APPEARS IN
संबंधित प्रश्न
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.
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 (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 (0, 0)
Find the equation of the parabola if the focus is at (0, −3) and the vertex is at (−1, −3)
Find the coordinates of points on the parabola y2 = 8x whose focal distance is 4.
If the line y = mx + 1 is tangent to the parabola y2 = 4x, then find the value of m.
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
The locus of the points of trisection of the double ordinates of a parabola is a
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 (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.
The equations of the lines joining the vertex of the parabola y2 = 6x to the points on it which have abscissa 24 are ______.
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.
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.
Find the equation of the following parabolas:
Directrix x = 0, focus at (6, 0)
Find the equation of the following parabolas:
Focus at (–1, –2), directrix x – 2y + 3 = 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.
The equation of the parabola having focus at (–1, –2) and the directrix x – 2y + 3 = 0 is ______.
The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity `1/2` is ______.
