What is 22y^2+32x^2-308y-512x+2.422=0 ?

The solution to 22y^2+32x^2-308y-512x+2.422=0 is Ellipse with (h,k)=(8,7),a=9.87986…,b=11.91557…

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22y^2+32x^2-308y-512x+2.422=0

22 y^{2} + 32 x^{2} - 308 y - 512 x + 2.422 = 0

(h, k) = (8, 7), a = 9.87986 \dots, b = 11.91557 \dots

Solution steps

22 y^{2} + 32 x^{2} - 308 y - 512 x + 2.422 = 0

Rewrite

22 y^{2} + 32 x^{2} - 308 y - 512 x + 2.422 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{9.87986 \dots ^{2}} + \frac{( y - 7 ) ^{2}}{11.91557 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, 7), a = 9.87986 \dots, b = 11.91557 \dots

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (8, 7), b = 11.91557 \dots, a = 9.87986 \dots

- 3 y^{2} - 3 x^{2} + 5 x + 10 y = 5 x^{2} + 1

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

(\frac{x - 5}{5})^{2} + (\frac{y + 7}{16})^{2} = 1

2 x^{2} + 4 y^{2} + 18 x + 24 y + 44 = 0

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

What is 22y^2+32x^2-308y-512x+2.422=0 ?
The solution to 22y^2+32x^2-308y-512x+2.422=0 is Ellipse with (h,k)=(8,7),a=9.87986…,b=11.91557…