Advertisements
Advertisements
प्रश्न
The vertex of the parabola (y − 2)2 = 16 (x − 1) is
पर्याय
(1, 2)
(−1, 2)
(1, −2)
(2, 1)
Advertisements
उत्तर
(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
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^2/16 + 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.
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.
4x2 + 9y2 = 36
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 parabola
y2 − 4y + 4x = 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
4 (y − 1)2 = − 7 (x − 3)
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.
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 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 \[\frac{\pi}{4}\]
If the coordinates of the vertex and focus of a parabola are (−1, 1) and (2, 3) respectively, then write the equation of its directrix.
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 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:
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).
Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, eccentricity, foci and vertices.
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 ______.
The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is ______.
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
The shortest distance from the point (2, –7) to the circle x2 + y2 – 14x – 10y – 151 = 0 is equal to 5.
