Find the vertex , focus, axis, directrix and latus rectum of the following parabola: `x^2+y=6x-14`

Explanation

`x^2 - 6x = - y - 14`

`x^2 - 6y + 9 = - y - 5`

`(x - 3)^2 = - (y + 5)`

Comparing with the standard form of parabola `(x - a)^2 = - 4b(y - c)` we get,

`4b=1=> b =frac{1}{4}`

The vertex is `(a, c) = (3, - 5)`

The focus is `(a, - b + c) = (3, frac{− 1 }{4 }) = (3, frac{− 21 }{4})`

The equation of the axis is `x - a = 0` i.e, `x - 3 = 0`
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