What is the axis x^2-6x-5y-1=0 ?

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axis x^2-6x-5y-1=0

axis

x^{2} - 6 x - 5 y - 1 = 0

x = 3

Solution steps

x^{2} - 6 x - 5 y - 1 = 0

Rewrite

x^{2} - 6 x - 5 y - 1 = 0

in the standard form

4 \cdot \frac{5}{4} (y - (- 2)) = (x - 3)^{2}

Therefore parabola properties are:

(h, k) = (3, - 2), p = \frac{5}{4}

Parabola is of the form

4 p (y - k) = (x - h)^{2}

and is symmetric around the

y

-axis

Axis of symmetry is a line parallel to the

y

-axis which intersects the vertex:

x = 3

y = + (x + 4)^{2} - 6

y = (x + 8)^{2}

(x + 3)^{2} = 24 (y - 1)

y = (z - 2)^{2}

3 x^{2} - 9 x - 2 = 5 y