What is y^2+5/2 y+(x^2)/4-44=0 ?

The solution to y^2+5/2 y+(x^2)/4-44=0 is Ellipse with (h,k)=(0,-5/4),a= 27/2 ,b= 27/4

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y^2+5/2 y+(x^2)/4-44=0

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

(h, k) = (0, - \frac{5}{4}), a = \frac{27}{2}, b = \frac{27}{4}

Solution steps

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

Rewrite

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{27}{2} ) ^{2}} + \frac{( y - ( - \frac{5}{4} ) ) ^{2}}{( \frac{27}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{5}{4}), a = \frac{27}{2}, b = \frac{27}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{5}{4}), a = \frac{27}{2}, b = \frac{27}{4}

\frac{x ^{2}}{100} + \frac{y ^{2}}{52} = 1

\frac{( x - 14 ) ^{2}}{3} + \frac{( y - 11 ) ^{2}}{4} = 1

x^{2} + 7 y^{2} = 12

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} < 1

What is y^2+5/2 y+(x^2)/4-44=0 ?
The solution to y^2+5/2 y+(x^2)/4-44=0 is Ellipse with (h,k)=(0,-5/4),a= 27/2 ,b= 27/4