Advertisements
Advertisements
Question
Write the axis of symmetry of the parabola y2 = x.
Solution
Clearly, the axis of symmetry of the given parabola is the x-axis.
APPEARS IN
RELATED QUESTIONS
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^2/16 + y^2/9 = 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^2/49 + y^2/36 = 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^2/100 + y^2/400 = 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.
36x2 + 4y2 = 144
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
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.
4x2 + 9y2 = 36
An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.
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
4x2 + y = 0
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 = 8x + 8y
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 5x − 4y − 9
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.
Write the length of the chord of the parabola y2 = 4ax which passes through the vertex and is inclined to the axis at \[\frac{\pi}{4}\]
The directrix of the parabola x2 − 4x − 8y + 12 = 0 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:
x2 + 4y2 − 4x + 24y + 31 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
4x2 + y2 − 8x + 2y + 1 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
4x2 + 16y2 − 24x − 32y − 12 = 0
Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:
x2 + 4y2 − 2x = 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.
Find the equation of the set of all points whose distances from (0, 4) are\[\frac{2}{3}\] of their distances from the line y = 9.
If the lengths of semi-major and semi-minor axes of an ellipse are 2 and \[\sqrt{3}\] and their corresponding equations are y − 5 = 0 and x + 3 = 0, then write the equation of the ellipse.
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.
Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, eccentricity, foci and vertices.
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 ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) 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.