What is 4x^2+5y^2+16x-20y+16=0 ?

The solution to 4x^2+5y^2+16x-20y+16=0 is Ellipse with (h,k)=(-2,2),a=sqrt(5),b=2

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4x^2+5y^2+16x-20y+16=0

4 x^{2} + 5 y^{2} + 16 x - 20 y + 16 = 0

(h, k) = (- 2, 2), a = 5, b = 2

Solution steps

4 x^{2} + 5 y^{2} + 16 x - 20 y + 16 = 0

Rewrite

4 x^{2} + 5 y^{2} + 16 x - 20 y + 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 2), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 2), a = 5, b = 2

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

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

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

4 (x - 4)^{2} + 9 (y - 2)^{2} = 36

\frac{( y + 7 ) ^{2}}{16} + \frac{( x - 5 ) ^{2}}{25} = 1

What is 4x^2+5y^2+16x-20y+16=0 ?
The solution to 4x^2+5y^2+16x-20y+16=0 is Ellipse with (h,k)=(-2,2),a=sqrt(5),b=2