What is 27x^2+48y^2-54x-192y-213=0 ?

The solution to 27x^2+48y^2-54x-192y-213=0 is Ellipse with (h,k)=(1,2),a=4,b=3

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27x^2+48y^2-54x-192y-213=0

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

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

Solution steps

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

Rewrite

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} + 16 y^{2} - 4 x - 128 y + 244 = 0

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

9 x^{(2)} + 16 y^{(2)} - 54 x + 64 y + 1 = 0

\frac{2 y}{1 - x ^{2} - y ^{2}} = 1

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

What is 27x^2+48y^2-54x-192y-213=0 ?
The solution to 27x^2+48y^2-54x-192y-213=0 is Ellipse with (h,k)=(1,2),a=4,b=3