What is x^2+2z^2+10x-16z+1=0 ?

The solution to x^2+2z^2+10x-16z+1=0 is Ellipse with (h,k)=(-5,4),a=2sqrt(14),b=2sqrt(7)

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x^2+2z^2+10x-16z+1=0

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

(h, k) = (- 5, 4), a = 214, b = 27

Solution steps

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

Rewrite

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 2 14 ) ^{2}} + \frac{( z - 4 ) ^{2}}{( 2 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 4), a = 214, b = 27

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, 4), a = 214, b = 27

\frac{x ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

9 > x^{2} + 9 y^{2}

27 x^{2} + 6 y^{2} - 5 = 0

- 1 = (\frac{( x - 0 )}{1 ^{2}})^{2} + (\frac{( y - 1 )}{1 ^{2}})^{2}

What is x^2+2z^2+10x-16z+1=0 ?
The solution to x^2+2z^2+10x-16z+1=0 is Ellipse with (h,k)=(-5,4),a=2sqrt(14),b=2sqrt(7)