Advertisements
Advertisements
प्रश्न
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
4x2 + y = 0
उत्तर
Given:
4x2 + y = 0
\[\Rightarrow \frac{- y}{4} = x^2\]
On comparing the given equation with \[x^2 = - 4ay\]
\[4a = \frac{1}{4} \Rightarrow a = \frac{1}{16}\]
∴ Vertex = (0, 0)
Focus = (0, −a) = \[\left( 0, \frac{- 1}{16} \right)\]
Equation of the directrix:
y = a
i.e. \[y = \frac{1}{16}\]
Axis = x = 0
Length of the latus rectum = 4a =\[\frac{1}{4}\]
APPEARS IN
संबंधित प्रश्न
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/36 + y^2/16 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/25 + y^2/100 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
16x2 + y2 = 16
A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola:
y2 = 8x
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas
y2 − 4y − 3x + 1 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 + 4x + 4y − 3 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 8x + 8y
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
x2 + y = 6x − 14
For the parabola y2 = 4px find the extremities of a double ordinate of length 8 p. Prove that the lines from the vertex to its extremities are at right angles.
Write the axis of symmetry of the parabola y2 = x.
Write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0.
Write the length of the chord of the parabola y2 = 4ax which passes through the vertex and is inclined to the axis at \[\frac{\pi}{4}\]
Write the coordinates of the vertex of the parabola whose focus is at (−2, 1) and directrix is the line x + y − 3 = 0.
In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is
The directrix of the parabola x2 − 4x − 8y + 12 = 0 is
The vertex of the parabola (y − 2)2 = 16 (x − 1) is
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
x2 + 2y2 − 2x + 12y + 10 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
3x2 + 4y2 − 12x − 8y + 4 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
4x2 + 16y2 − 24x − 32y − 12 = 0
Find the equation of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1).
A rod of length 12 m moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with x-axis.
Write the eccentricity of the ellipse 9x2 + 5y2 − 18x − 2y − 16 = 0.
PSQ is a focal chord of the ellipse 4x2 + 9y2 = 36 such that SP = 4. If S' is the another focus, write the value of S'Q.
If S and S' are two foci of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and B is an end of the minor axis such that ∆BSS' is equilateral, then write the eccentricity of the ellipse.
If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse.
Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, eccentricity, foci and vertices.
Find the equation of the ellipse with foci at (± 5, 0) and x = `36/5` as one of the directrices.
The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is ______.
The equation of the circle having centre (1, –2) and passing through the point of intersection of the lines 3x + y = 14 and 2x + 5y = 18 is ______.
If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle.
Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1
The shortest distance from the point (2, –7) to the circle x2 + y2 – 14x – 10y – 151 = 0 is equal to 5.
