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

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

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

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

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

Solution steps

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

Rewrite

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

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, x^{2} + \frac{π R ( x ) ^{2}}{2} = 200

\frac{( x ^{2} )}{( 29 )} + \frac{( y ^{2} )}{( 24 )} = 1

36 x^{2} + 16 y^{2} + 96 y - 180 x - 207 = 0

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

7 x^{2} - 28 x + 4 y^{2} + 8 y = - 4

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