What is 9x^2+4y^2+36x+16y+16=0 ?

The solution to 9x^2+4y^2+36x+16y+16=0 is Ellipse with (h,k)=(-2,-2),a=2,b=3

Popular >

9x^2+4y^2+36x+16y+16=0

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

(h, k) = (- 2, - 2), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

Rewrite

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 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, - 2), b = 3, a = 2

(\frac{x - 2}{4})^{2} + (\frac{y + 3}{16})^{2} = 1

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{4} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{\frac{25}{4}} = 1

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

5 x^{2} + 2 y^{2} = 98

What is 9x^2+4y^2+36x+16y+16=0 ?
The solution to 9x^2+4y^2+36x+16y+16=0 is Ellipse with (h,k)=(-2,-2),a=2,b=3