What is 4x^2+8x+9(y-2)^2=32 ?

The solution to 4x^2+8x+9(y-2)^2=32 is Ellipse with (h,k)=(-1,2),a=3,b=2

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4x^2+8x+9(y-2)^2=32

4 x^{2} + 8 x + 9 (y - 2)^{2} = 32

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

Solution steps

4 x^{2} + 8 x + 9 (y - 2)^{2} = 32

Rewrite

4 x^{2} + 8 x + 9 (y - 2)^{2} = 32

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 + 3 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{16} = 1

16 x^{2} + 64 x + 4 y^{2} - 8 y + 4 = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

49 x^{2} + 4 y^{2} = 196

18 y^{2} + 24 y + 12 x^{2} - 12 x = 1

What is 4x^2+8x+9(y-2)^2=32 ?
The solution to 4x^2+8x+9(y-2)^2=32 is Ellipse with (h,k)=(-1,2),a=3,b=2