What is (x^2+9x)+(4y^2+10)=5 ?

The solution to (x^2+9x)+(4y^2+10)=5 is Ellipse with (h,k)=(-9/2 ,0),a=(sqrt(61))/2 ,b=(sqrt(61))/4

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(x^2+9x)+(4y^2+10)=5

(x^{2} + 9 x) + (4 y^{2} + 10) = 5

(h, k) = (- \frac{9}{2}, 0), a = \frac{61}{2}, b = \frac{61}{4}

Solution steps

x^{2} + 9 x + (4 y^{2} + 10) = 5

Rewrite

x^{2} + 9 x + (4 y^{2} + 10) = 5

in the form of the standard ellipse equation

\frac{( x - ( - \frac{9}{2} ) ) ^{2}}{( \frac{61}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{61}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{9}{2}, 0), a = \frac{61}{2}, b = \frac{61}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{9}{2}, 0), a = \frac{61}{2}, b = \frac{61}{4}

\frac{( x - 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

1 - x^{2} - 5 y^{2} > 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{16} = 1

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

What is (x^2+9x)+(4y^2+10)=5 ?
The solution to (x^2+9x)+(4y^2+10)=5 is Ellipse with (h,k)=(-9/2 ,0),a=(sqrt(61))/2 ,b=(sqrt(61))/4