Find the centre, eccentricity, foci and directrices of the hyperbola : `x^2-y^2+4x=0`

Explanation

We Have given `x^2 – y^2+4x=0`

And to find the center, eccentricity(e), coordinates of the foci f(m, n), equation of directrix. `x^2 – y^2 +4x = 0`
implies `x^2 + 4x + 4 – y^2 – 4 = 0`

`implies ((x+2)^2)/4 – (y^2)/4 = 1`

`implies ((x+2)^2)/(2^2) – (y^2)/(2^2) = 1`

As the center of the hyperbola is `(2, 0)`

Then let `x –2=X`

Now we know the formula for hyperbola as `(x^2/a^2) - (y^2/b^2) = 1`

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