What is 36x^2+y^2+2y+1=9 ?

The solution to 36x^2+y^2+2y+1=9 is Ellipse with (h,k)=(0,-1),a= 1/2 ,b=3

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36x^2+y^2+2y+1=9

36 x^{2} + y^{2} + 2 y + 1 = 9

(h, k) = (0, - 1), a = \frac{1}{2}, b = 3

Solution steps

36 x^{2} + y^{2} + 2 y + 1 = 9

Rewrite

36 x^{2} + y^{2} + 2 y + 1 = 9

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 1), a = \frac{1}{2}, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 3, a = \frac{1}{2}

(4 x^{2}) + (y^{2}) - 8 x - 4 y - 28 = 0

112 x^{2} + 144 y^{2} - 896 x + 864 y = - 2080

8 x^{2} + y^{2} = 1

9 = 4 x^{2} + z^{2}

\frac{x ^{2}}{4} + \frac{y ^{2}}{6} = 1

What is 36x^2+y^2+2y+1=9 ?
The solution to 36x^2+y^2+2y+1=9 is Ellipse with (h,k)=(0,-1),a= 1/2 ,b=3