What is 18x^2-72x+4y^2+4y+37=0 ?

The solution to 18x^2-72x+4y^2+4y+37=0 is Ellipse with (h,k)=(2,-1/2),a=sqrt(2),b=3

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18x^2-72x+4y^2+4y+37=0

18 x^{2} - 72 x + 4 y^{2} + 4 y + 37 = 0

(h, k) = (2, - \frac{1}{2}), a = 2, b = 3

Solution steps

18 x^{2} - 72 x + 4 y^{2} + 4 y + 37 = 0

Rewrite

18 x^{2} - 72 x + 4 y^{2} + 4 y + 37 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - \frac{1}{2}), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - \frac{1}{2}), b = 3, a = 2

6 (x + 1)^{2} + 2 (y - 1)^{2} = 72

\frac{( x - \frac{5}{2} ) ^{2}}{9} + \frac{y ^{2}}{49} = 1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{16} = 1

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

2 = \frac{x ^{2}}{4} + \frac{y ^{2}}{9}

What is 18x^2-72x+4y^2+4y+37=0 ?
The solution to 18x^2-72x+4y^2+4y+37=0 is Ellipse with (h,k)=(2,-1/2),a=sqrt(2),b=3