What is x^2=9+8y-4y^2 ?

The solution to x^2=9+8y-4y^2 is Ellipse with (h,k)=(0,1),a=sqrt(13),b=(sqrt(13))/2

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x^2=9+8y-4y^2

x^{2} = 9 + 8 y - 4 y^{2}

(h, k) = (0, 1), a = 13, b = \frac{13}{2}

Solution steps

x^{2} = 9 + 8 y - 4 y^{2}

Rewrite

x^{2} = 9 + 8 y - 4 y^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 13 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 13, b = \frac{13}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 1), a = 13, b = \frac{13}{2}

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 2 ) ^{2}}{9} = 1

16 x^{2} - 64 x + 25 y^{2} + 150 y = 111

\frac{x ^{2}}{100} + \frac{y ^{2}}{25} = 1

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

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

What is x^2=9+8y-4y^2 ?
The solution to x^2=9+8y-4y^2 is Ellipse with (h,k)=(0,1),a=sqrt(13),b=(sqrt(13))/2