What is 25x^2+9y^2+200x-36y+211=0 ?

The solution to 25x^2+9y^2+200x-36y+211=0 is Ellipse with (h,k)=(-4,2),a=3,b=5

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25x^2+9y^2+200x-36y+211=0

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

(h, k) = (- 4, 2), a = 3, b = 5

Solution steps

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

Rewrite

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{3 ^{2}} + \frac{( y - 2 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 2), a = 3, 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 = 3

4 x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

- 5 x^{2} - 6 y^{2} = 1

\frac{( x + 2 ) ^{2}}{( - 13 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( - 8 ) ^{2}} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 25

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

What is 25x^2+9y^2+200x-36y+211=0 ?
The solution to 25x^2+9y^2+200x-36y+211=0 is Ellipse with (h,k)=(-4,2),a=3,b=5