Advertisements
Advertisements
प्रश्न
The equation 16x2 + y2 + 8xy − 74x − 78y + 212 = 0 represents
पर्याय
a circle
a parabola
an ellipse
a hyperbola
Advertisements
उत्तर
a parabola
Comparing the given equation with ax2 + by2 + 2hxy + 2gx+2fy + c =0, we get:
\[a = 16, b = 1, h = 4\]
We have:
\[h^2 = 16 = ab\]
Thus, the given equation represents a parabola.
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 (0, –3); directrix y = 3
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) 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 (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 (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 (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).
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).
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.
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 parametric equations of a parabola are x = t2 + 1, y = 2t + 1. The cartesian equation of its directrix is
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 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.
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:
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 ______.
The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity `1/2` is ______.
