Advertisements
Advertisements
Question
The vertex of the parabola (y − 2)2 = 16 (x − 1) is
Options
(1, 2)
(−1, 2)
(1, −2)
(2, 1)
Solution
(1, 2)
Given:
(y − 2)2 = 16 (x − 1)
Let \[X = x - 1, Y = y - 2\]
∴ \[Y^2 = 16X\]
Vertex = \[\left( X = 0, Y = 0 \right) = \left( x - 1 = 0, y - 2 = 0 \right) = \left( x = 1, y = 2 \right)\]
Hence, the vertex is at (1, 2).
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^2/36 + 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.
`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 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 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 − 4y + 4x = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 + 4x + 4y − 3 = 0
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 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 \[\frac{\pi}{4}\]
In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is
The equation of the parabola with focus (0, 0) and directrix x + y = 4 is
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 equation of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1).
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.
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 ______.
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 equation of a circle which touches both the axes and the line 3x – 4y + 8 = 0 and lies in the third quadrant.
Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1
