What is 4x^2+16y^2+16x+160y+352=0 ?

The solution to 4x^2+16y^2+16x+160y+352=0 is Ellipse with (h,k)=(-2,-5),a=4,b=2

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4x^2+16y^2+16x+160y+352=0

4 x^{2} + 16 y^{2} + 16 x + 160 y + 352 = 0

(h, k) = (- 2, - 5), a = 4, b = 2

Solution steps

4 x^{2} + 16 y^{2} + 16 x + 160 y + 352 = 0

Rewrite

4 x^{2} + 16 y^{2} + 16 x + 160 y + 352 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 5), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 5), a = 4, b = 2

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

\frac{( x + 9 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{9} = 1

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

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

7 x^{2} + 16 y^{2} - 112 = 0

What is 4x^2+16y^2+16x+160y+352=0 ?
The solution to 4x^2+16y^2+16x+160y+352=0 is Ellipse with (h,k)=(-2,-5),a=4,b=2