What is x^2-2x+(y^2)/4-y=14 ?

The solution to x^2-2x+(y^2)/4-y=14 is Ellipse with (h,k)=(1,2),a=4,b=8

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x^2-2x+(y^2)/4-y=14

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

(h, k) = (1, 2), a = 4, b = 8

Solution steps

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

Rewrite

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{4 ^{2}} + \frac{( y - 2 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 2), a = 4, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 8, a = 4

\frac{( x + 1 ) ^{2}}{28} + \frac{( y + 5 ) ^{2}}{23} = 1

2 x^{2} + y^{2} + 12 x - 2 y + 17 = 0

y^{2} + 2 y + 6 x^{2} - 12 x = 1

x^{2} + 2 y^{2} - 2 x - 4 y - 5 = 0

x^{2} + 9 y^{2} + 90 y + 189 = 0

What is x^2-2x+(y^2)/4-y=14 ?
The solution to x^2-2x+(y^2)/4-y=14 is Ellipse with (h,k)=(1,2),a=4,b=8