Question

Identify the type of conic and find centre, foci, vertices, and directrices of the following:

`(x + 1)^2/100 + (y - 2)^2/64` = 1

Answer 1

It is an ellipse.

The major axis is parallel to the x-axis.

a² = 100, b² = 64

a = 10, b = 8

c² = a² – b²

= 100 – 64 = 36

c = 6

ae = 6

10e = 6

e = `6/10 = 3/5`

Centre (h, k) = (– 1, 2)

Vertices (h ± a, k) = (– 1 ± 10, 2)

= (– 1 + 10, 2) and (– 1 – 10, 2)

= (9, 2) and (– 11, 2)

Foci (h ± c, k) = (– 1 ± 6, 2)

= (– 1 + 6, 2) and (– 1 – 6, 2)

= (5, 2) and (– 7, 2)

Directrix x = `+-  "a"/"e" + "h"`

= `+-  10/(3/5) - 1`

= `+-  50/3 - 1`

x = `50/3 - 1` and x = `50/(-3) - 1`

= `47/3`  and `(- 53)/5`