What is 4x^2+16x+5y^2-10y+1=0 ?

The solution to 4x^2+16x+5y^2-10y+1=0 is Ellipse with (h,k)=(-2,1),a=sqrt(5),b=2

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4x^2+16x+5y^2-10y+1=0

4 x^{2} + 16 x + 5 y^{2} - 10 y + 1 = 0

(h, k) = (- 2, 1), a = 5, b = 2

Solution steps

4 x^{2} + 16 x + 5 y^{2} - 10 y + 1 = 0

Rewrite

4 x^{2} + 16 x + 5 y^{2} - 10 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), a = 5, b = 2

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

x^{2} + 4 y^{2} = 20

8 x^{2} + z^{2} = 36

\frac{( x - 1.23 ) ^{2}}{1.4 1 ^{2}} + \frac{y ^{2}}{1.00 7 ^{2}} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{5} = 1

What is 4x^2+16x+5y^2-10y+1=0 ?
The solution to 4x^2+16x+5y^2-10y+1=0 is Ellipse with (h,k)=(-2,1),a=sqrt(5),b=2