What is 25x^2+16y^2-350x+96y-231=0 ?

The solution to 25x^2+16y^2-350x+96y-231=0 is Ellipse with (h,k)=(7,-3),a=8,b=10

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25x^2+16y^2-350x+96y-231=0

25 x^{2} + 16 y^{2} - 350 x + 96 y - 231 = 0

(h, k) = (7, - 3), a = 8, b = 10

Solution steps

25 x^{2} + 16 y^{2} - 350 x + 96 y - 231 = 0

Rewrite

25 x^{2} + 16 y^{2} - 350 x + 96 y - 231 = 0

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{8 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, - 3), a = 8, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (7, - 3), b = 10, a = 8

4 x^{2} + 3 y^{2} - 12 = 0

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

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y = 59

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0

What is 25x^2+16y^2-350x+96y-231=0 ?
The solution to 25x^2+16y^2-350x+96y-231=0 is Ellipse with (h,k)=(7,-3),a=8,b=10