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Question
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/3 + y^2/10` = 1
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)`
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