What is 9(x+yi)^2+9(x-yi)^2+82(x+yi)(x-yi)=1600 ?

The solution to 9(x+yi)^2+9(x-yi)^2+82(x+yi)(x-yi)=1600 is Ellipse with (h,k)=(0,0),a=4,b=5

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9(x+yi)^2+9(x-yi)^2+82(x+yi)(x-yi)=1600

9 (x + y i)^{2} + 9 (x - y i)^{2} + 82 (x + y i) (x - y i) = 1600

(h, k) = (0, 0), a = 4, b = 5

Solution steps

9 (x + y i)^{2} + 9 (x - y i)^{2} + 82 (x + y i) (x - y i) = 1600

Rewrite

9 (x + y i)^{2} + 9 (x - y i)^{2} + 82 (x + y i) (x - y i) = 1600

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 4

x^{2} + 4 y^{2} + 8 x - 24 y - 92 = 0

16 (x - 8)^{2} + 64 (y - 4)^{2} = 1024

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

\frac{x ^{2} + x + y ^{2} - 1}{2 \cdot y} = \frac{1}{4}

25 x^{2} + 9 y^{2} + 50 x - 54 y - 119 = 0

What is 9(x+yi)^2+9(x-yi)^2+82(x+yi)(x-yi)=1600 ?
The solution to 9(x+yi)^2+9(x-yi)^2+82(x+yi)(x-yi)=1600 is Ellipse with (h,k)=(0,0),a=4,b=5