Advertisements
Advertisements
Question
The vertex of the parabola x2 + 8x + 12y + 4 = 0 is
Options
(−4, 1)
(4, −1)
(−4, −1)
(4, 1)
Solution
(−4, 1)
Given:
x2 + 8x + 12y + 4 = 0
\[\Rightarrow \left( x + 4 \right)^2 - 16 + 12y + 4 = 0\]
\[ \Rightarrow \left( x + 4 \right)^2 + 12y - 12 = 0\]
\[ \Rightarrow \left( x + 4 \right)^2 = - 12\left( y - 1 \right)\]
Let \[X = x + 4, Y = y - 1\]
∴ \[X^2 = - 12Y\]
Vertex = \[\left( X = 0, Y = 0 \right) = \left( x + 4 = 0, y - 1 = 0 \right) = \left( x = - 4, y = 1 \right)\]
Hence, the vertex is at (−4, 1).
APPEARS IN
RELATED QUESTIONS
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.
y2 = 12x
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.
x2 = – 16y
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.
y2 = 10x
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum.
x2 = –9y
Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.
Find the area of the triangle formed by the lines joining the vertex of the parabola \[x^2 = 12y\] to the ends of its latus rectum.
Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3, 3) and directrix is 3x − 4y = 2. Find also the length of the latus-rectum.
If b and c are lengths of the segments of any focal chord of the parabola y2 = 4ax, then write the length of its latus-rectum.
(vii) find the equation of the hyperbola satisfying the given condition:
foci (± 4, 0), the latus-rectum = 12
If the parabola y2 = 4ax passes through the point (3, 2), then find the length of its latus rectum.
The vertex of the parabola (y + a)2 = 8a (x − a) is
If the focus of a parabola is (−2, 1) and the directrix has the equation x + y = 3, then its vertex is
The length of the latus-rectum of the parabola y2 + 8x − 2y + 17 = 0 is
The length of the latus-rectum of the parabola 4y2 + 2x − 20y + 17 = 0 is
The length of the latus-rectum of the parabola x2 − 4x − 8y + 12 = 0 is
The focus of the parabola y = 2x2 + x is
Which of the following points lie on the parabola x2 = 4ay?
The area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum is ______.
If the latus rectum of an ellipse with axis along x-axis and centre at origin is 10, distance between foci = length of minor axis, then the equation of the ellipse is ______.
If the eccentricity of an ellipse is `5/8` and the distance between its foci is 10, then find latus rectum of the ellipse.
If the parabola y2 = 4ax passes through the point (3, 2), then the length of its latus rectum is ______.
