What is x^2+9y^2+8x-36y+43=0 ?

The solution to x^2+9y^2+8x-36y+43=0 is Ellipse with (h,k)=(-4,2),a=3,b=1

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x^2+9y^2+8x-36y+43=0

x^{2} + 9 y^{2} + 8 x - 36 y + 43 = 0

(h, k) = (- 4, 2), a = 3, b = 1

Solution steps

x^{2} + 9 y^{2} + 8 x - 36 y + 43 = 0

Rewrite

x^{2} + 9 y^{2} + 8 x - 36 y + 43 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 2), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 2), a = 3, b = 1

\frac{( x + 7 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

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

16 x^{2} + 96 x + 25 y^{2} + 100 y - 156 = 0

3 x^{2} - 6 x + y^{2} + 4 y - 2 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{81} = 1

What is x^2+9y^2+8x-36y+43=0 ?
The solution to x^2+9y^2+8x-36y+43=0 is Ellipse with (h,k)=(-4,2),a=3,b=1