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Question
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 + y^2/9` = 1
Solution
It is of the form `x^2/25 + y^2/9` = 1
which is an ellipse
Here a2 = 25, b2 = 9
a = 5, b = 3
e2 = `("a"^2 - "b"^2)/"a"^2`
= `(25 - 9)/25`
= `16/25`
⇒ e = `4/5`
Now e = `4/5` and a = 5
⇒ ae = 4 and `"a"/"e" = 5/(4/5) = 25/4`
Here the major axis is along x axis
∴ Centre = (0, 0)
Foci = (± ae, 0) = (± 4, 0)
Vertices = (± a, 0) = (±5, 0)
Equation of directrix x = `+- "a"/"e"`
(i.e,) x = `+- 25/4`
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