What is 25x^2+4y^2+200x-8y+304=0 ?

The solution to 25x^2+4y^2+200x-8y+304=0 is Ellipse with (h,k)=(-4,1),a=2,b=5

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25x^2+4y^2+200x-8y+304=0

25 x^{2} + 4 y^{2} + 200 x - 8 y + 304 = 0

(h, k) = (- 4, 1), a = 2, b = 5

Solution steps

25 x^{2} + 4 y^{2} + 200 x - 8 y + 304 = 0

Rewrite

25 x^{2} + 4 y^{2} + 200 x - 8 y + 304 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 1), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, 1), b = 5, a = 2

(x - 3)^{2} + 16 (y - 2)^{2} = 16

\frac{( 2 x + 1 ) ^{2}}{4} + \frac{( 3 y - 2 ) ^{2}}{16} = 1

\frac{( x + 1 ) ^{2}}{100} + \frac{( y + 2 ) ^{2}}{121} = 1

25 x^{2} + 16 y^{2} < 400

x^{2} + y^{2} = 6 y - 8 y

What is 25x^2+4y^2+200x-8y+304=0 ?
The solution to 25x^2+4y^2+200x-8y+304=0 is Ellipse with (h,k)=(-4,1),a=2,b=5