What is 4x^2+9y^2+8x-36y+4=0 ?

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

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4x^2+9y^2+8x-36y+4=0

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

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

Solution steps

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

Rewrite

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 2 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{9} = 1

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

\frac{( x + 1 ) ^{2}}{28} + \frac{( y + 5 ) ^{2}}{23} = 1

2 x^{2} + y^{2} + 12 x - 2 y + 17 = 0

y^{2} + 2 y + 6 x^{2} - 12 x = 1

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