What is x^2+2-6x=-5z^2+2 ?

The solution to x^2+2-6x=-5z^2+2 is Ellipse with (h,k)=(3,0),a=3,b= 3/(sqrt(5))

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x^2+2-6x=-5z^2+2

x^{2} + 2 - 6 x = - 5 z^{2} + 2

(h, k) = (3, 0), a = 3, b = \frac{3}{5}

Solution steps

x^{2} + 2 - 6 x = - 5 z^{2} + 2

Rewrite

x^{2} + 2 - 6 x + 5 z^{2} - 2 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{3 ^{2}} + \frac{( z - 0 ) ^{2}}{( \frac{3}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 0), a = 3, b = \frac{3}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 0), a = 3, b = \frac{3}{5}

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

x, x^{2} + 5 Y (x)^{2} + 2 x - 30 Y + 36 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{49} = 1

\frac{( x - 1 ) ^{2}}{8} + \frac{( y + \frac{3}{2} ) ^{2}}{4} = 1

11 x^{2} + 9 y^{2} = 1

What is x^2+2-6x=-5z^2+2 ?
The solution to x^2+2-6x=-5z^2+2 is Ellipse with (h,k)=(3,0),a=3,b= 3/(sqrt(5))