What is the axis y^2-8x-6y-3=0 ?

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axis y^2-8x-6y-3=0

axis

y^{2} - 8 x - 6 y - 3 = 0

y = 3

Solution steps

y^{2} - 8 x - 6 y - 3 = 0

Rewrite

y^{2} - 8 x - 6 y - 3 = 0

in the standard form

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

Therefore parabola properties are:

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

Parabola is of the form

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

and is symmetric around the

x

-axis

Axis of symmetry is a line parallel to the

x

-axis which intersects the vertex:

y = 3

y = 6 x^{2} + 10 x - 4

y = - 2 x^{2} + 16 x - 31

y = 4 x^{2} + x + 1

y = + 1 - x - x^{2}

x = \frac{y ^{2}}{8}