Advertisements
Advertisements
Question
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x - 3)^2/225 + (y - 4)^2/289` = 1
Advertisements
Solution
It is an ellipse.
The major axis is parallel to y axis
a2 = 289, b2 = 225
a = 17, b = 15
c2 = a2 – b2
= 289 – 225 = 64
c = 8
ae = 8
17e = 8
e = `8/17`
Vertices (h, ±a + k)
= (3, 17 + 4) and (3, – 17 + 4)!
= (3, 21) and (3, – 13)
Foci (h + 0, ± c + k)
= (3, 8 + 4) and (3, – 8 + 4)
= (3, 12) and (3, – 4)
Directrices y = `+- "a"/"e" + "k"`
= `+- 17/(8/17) + 4`
= `+- 289/8 + 4`
= `289/8 + 4` and `- 289/8 + 4`
= `(289 + 32)/8` and `(- 289 + 32)/8`
= `321/8` and `- 257/8`
APPEARS IN
RELATED QUESTIONS
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = - 16y
Find the equation of the parabola which is symmetrical about x-axis and passing through (–2, –3).
The equation of directrix of the parabola y2 = -x is:
Find the equation of the parabola in the cases given below:
Focus (4, 0) and directrix x = – 4
Find the equation of the parabola in the cases given below:
Vertex (1, – 2) and Focus (4, – 2)
Find the equation of the ellipse in the cases given below:
Foci `(+- 3, 0), "e"+ 1/2`
Find the equation of the ellipse in the cases given below:
Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis
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:
y2 – 4y – 8x + 12 = 0
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 + y^2/9` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 1
Prove that the length of the latus rectum of the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 is `(2"b"^2)/"a"`
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:
18x2 + 12y2 – 144x + 48y + 120 = 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
The fixed straight line used in the definition of a conic section is called the:
If the eccentricity e > 1, the conic section is:
A chord passing through any point on the conic and perpendicular to the axis is called:
