What is (x^2}{16}+x/2+\frac{y^2)/4+y+1=0 ?

The solution to (x^2}{16}+x/2+\frac{y^2)/4+y+1=0 is Ellipse with (h,k)=(-4,-2),a=4,b=2

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(x^2}{16}+x/2+\frac{y^2)/4+y+1=0

\frac{x ^{2}}{16} + \frac{x}{2} + \frac{y ^{2}}{4} + y + 1 = 0

(h, k) = (- 4, - 2), a = 4, b = 2

Solution steps

\frac{x ^{2}}{16} + \frac{x}{2} + \frac{y ^{2}}{4} + y + 1 = 0

Rewrite

\frac{x ^{2}}{16} + \frac{x}{2} + \frac{y ^{2}}{4} + y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, - 2), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 4 y^{2} - 27 x + 16 y - 119 = 0

x^{2} + 5 y^{2} + 2 x - 30 y + 36 = 0

\frac{x ^{2}}{64} + \frac{y ^{2}}{39} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{2} = 1

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

What is (x^2}{16}+x/2+\frac{y^2)/4+y+1=0 ?
The solution to (x^2}{16}+x/2+\frac{y^2)/4+y+1=0 is Ellipse with (h,k)=(-4,-2),a=4,b=2