What is 25x^2+16y^2+200x+64y+64=0 ?

The solution to 25x^2+16y^2+200x+64y+64=0 is Ellipse with (h,k)=(-4,-2),a=4,b=5

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25x^2+16y^2+200x+64y+64=0

25 x^{2} + 16 y^{2} + 200 x + 64 y + 64 = 0

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

Solution steps

25 x^{2} + 16 y^{2} + 200 x + 64 y + 64 = 0

Rewrite

25 x^{2} + 16 y^{2} + 200 x + 64 y + 64 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

27 x^{2} + 48 y^{2} - 54 x - 192 y - 213 = 0

x^{2} + 16 y^{2} - 4 x - 128 y + 244 = 0

2 x^{2} - 4 x + y^{2} = 0

9 x^{(2)} + 16 y^{(2)} - 54 x + 64 y + 1 = 0

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

What is 25x^2+16y^2+200x+64y+64=0 ?
The solution to 25x^2+16y^2+200x+64y+64=0 is Ellipse with (h,k)=(-4,-2),a=4,b=5