What is the axis x^2+10x-2y+21=0 ?

The axis x^2+10x-2y+21=0 is x=-5

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axis x^2+10x-2y+21=0

axis

x^{2} + 10 x - 2 y + 21 = 0

x = - 5

Solution steps

x^{2} + 10 x - 2 y + 21 = 0

Rewrite

x^{2} + 10 x - 2 y + 21 = 0

in the standard form

4 \cdot \frac{1}{2} (y - (- 2)) = (x - (- 5))^{2}

Therefore parabola properties are:

(h, k) = (- 5, - 2), p = \frac{1}{2}

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 = - 5

y = - 2 (x - 4)^{2} + 5

x = (y + 1) (y + 2)

4 x^{2} - 128 y = 0

(y - 3)^{2} = - 8 (x - 4)

y = (x - 13)^{2}