What is 4x^2+y^2-6y=27 ?

The solution to 4x^2+y^2-6y=27 is Ellipse with (h,k)=(0,3),a=3,b=6

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4x^2+y^2-6y=27

4 x^{2} + y^{2} - 6 y = 27

(h, k) = (0, 3), a = 3, b = 6

Solution steps

4 x^{2} + y^{2} - 6 y = 27

Rewrite

4 x^{2} + y^{2} - 6 y = 27

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 3 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 3), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 3), b = 6, a = 3

8 x^{2} + 16 x + 2 y^{2} = 0

4 x^{2} + 36 y^{2} + 24 x + 432 y = - 1188

\frac{( x - 3 ) ^{2}}{100} + \frac{( y + 4 ) ^{2}}{64} = 1

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

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

What is 4x^2+y^2-6y=27 ?
The solution to 4x^2+y^2-6y=27 is Ellipse with (h,k)=(0,3),a=3,b=6