What is 16x^2+25y^2+160x+200y+400=0 ?

The solution to 16x^2+25y^2+160x+200y+400=0 is Ellipse with (h,k)=(-5,-4),a=5,b=4

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16x^2+25y^2+160x+200y+400=0

16 x^{2} + 25 y^{2} + 160 x + 200 y + 400 = 0

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

Solution steps

16 x^{2} + 25 y^{2} + 160 x + 200 y + 400 = 0

Rewrite

16 x^{2} + 25 y^{2} + 160 x + 200 y + 400 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

What is 16x^2+25y^2+160x+200y+400=0 ?
The solution to 16x^2+25y^2+160x+200y+400=0 is Ellipse with (h,k)=(-5,-4),a=5,b=4