Advertisements
Advertisements
Question
Find the equation of the parabola in the cases given below:
Focus (4, 0) and directrix x = – 4
Solution
Focus (4, 0) and directrix x = – 4
Parabola is open rightwards vertex (0, 0)
a = 4
Distance AS = 4 unit
F2 = 4(4)x
Equation of parabola
y2 = 16x.
APPEARS IN
RELATED QUESTIONS
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
The focus of the parabola x2 = 16y is:
The double ordinate passing through the focus is:
Find the equation of the ellipse in the cases given below:
Foci (0, ±4) and end points of major axis are (0, ±5)
Find the equation of the ellipse in the cases given below:
Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis
Find the equation of the hyperbola in the cases given below:
Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 = 16x
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x2 – 2x + 8y + 17 = 0
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 – 4y – 8x + 12 = 0
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/3 + y^2/10` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 1
Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x + 1)^2/100 + (y - 2)^2/64` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x + 3)^2/225 + (y - 4)^2/64` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(y - 2)^3/25 + (x + 1)^2/16` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
9x2 – y2 – 36x – 6y + 18 = 0
Choose the correct alternative:
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is
Choose the correct alternative:
If x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
