What is x^2+2y^2-10x+8y+29=0 ?

The solution to x^2+2y^2-10x+8y+29=0 is Ellipse with (h,k)=(5,-2),a=2,b=sqrt(2)

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x^2+2y^2-10x+8y+29=0

x^{2} + 2 y^{2} - 10 x + 8 y + 29 = 0

(h, k) = (5, - 2), a = 2, b = 2

Solution steps

x^{2} + 2 y^{2} - 10 x + 8 y + 29 = 0

Rewrite

x^{2} + 2 y^{2} - 10 x + 8 y + 29 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 2), a = 2, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 2), a = 2, b = 2

16 x^{2} + 4 y^{2} - 32 x + 16 y - 32 = 0

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

\frac{( x - 5 ) ^{2}}{49} + \frac{( y + 4 ) ^{2}}{81} = 1

x^{2} + 9 y^{2} \leq 16

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

What is x^2+2y^2-10x+8y+29=0 ?
The solution to x^2+2y^2-10x+8y+29=0 is Ellipse with (h,k)=(5,-2),a=2,b=sqrt(2)