Advertisements
Advertisements
Question
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/3 + y^2/10` = 1
Advertisements
Solution
It is an ellipse.
The major axis is along y-axis
a2 = 10, b2 = 3
a = `sqrt(10)`, b = `sqrt(3)`
c2 = a2 – b2
= 10 – 3
= 7
c = `sqrt(7)`
ae = `sqrt(7)`
`sqrt(10) = sqrt(7)`
e = `sqrt(7/10)`
(a) Centre (0, 0)
(b) Vertex (0, ± a) = `(0, +- sqrt(10))`
(c) Foci (0, ± c) – `(0, +- sqrt(7))`
(d) Equation of the directrix a
y = `+- "a"/"e"`
= `+- sqrt(10)/sqrt(7) * sqrt(10)`
= `+- 10/sqrt(7)`
y = `+- 10/sqrt(7)`
APPEARS IN
RELATED QUESTIONS
Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.
Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = 8y
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = - 16y
The average variable cost of the monthly output of x tonnes of a firm producing a valuable metal is ₹ `1/5`x2 – 6x + 100. Show that the average variable cost curve is a parabola. Also, find the output and the average cost at the vertex of the parabola.
The eccentricity of the parabola is:
The double ordinate passing through the focus is:
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:
x2 – 2x + 8y + 17 = 0
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 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:
18x2 + 12y2 – 144x + 48y + 120 = 0
Choose the correct alternative:
If P(x, y) be any point on 16x2 + 25y2 = 400 with foci F(3, 0) then PF1 + PF2 is
Choose the correct alternative:
If x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
Which statement best describes a focal chord in any conic section?
The latus-rectum of a conic section is:
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:
