What is x^2+10x+9y^2+16=0 ?

The solution to x^2+10x+9y^2+16=0 is Ellipse with (h,k)=(-5,0),a=3,b=1

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x^2+10x+9y^2+16=0

x^{2} + 10 x + 9 y^{2} + 16 = 0

(h, k) = (- 5, 0), a = 3, b = 1

Solution steps

x^{2} + 10 x + 9 y^{2} + 16 = 0

Rewrite

x^{2} + 10 x + 9 y^{2} + 16 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 0), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, 0), a = 3, b = 1

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

\frac{x ^{2}}{7 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

16 x^{2} + 25 y^{2} = 1600

4 x^{2} + 9 y^{2} - 8 x - 32 = 0

What is x^2+10x+9y^2+16=0 ?
The solution to x^2+10x+9y^2+16=0 is Ellipse with (h,k)=(-5,0),a=3,b=1