Find the vertex , focus, axis, directrix and latus rectum of the following parabola: `y^2=5x-4y-9`

Explanation

Given equation of the parabola is `y^2 = 5x - 4y - 9`.

`y^2 + 4y = 5x - 9`

` y^2 + 4y + 4 = 5x - 5`

`(y + 2)^2 = 5(x - 1)`

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

` 4b = 5 ⇒ b = frac{5}{4}`
The vertex is `(c, a) = (1, - 2) `

The focus is `(b + c, a)= ( frac{5}{4} + 1,-2) = ( frac{9}{ 4},-2)`

The equation of the axis is `y - a = 0` i.e, `y + 2 = 0`
...