What is 25x^2+16y^2+50x-96y-231=0 ?

The solution to 25x^2+16y^2+50x-96y-231=0 is Ellipse with (h,k)=(-1,3),a=4,b=5

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25x^2+16y^2+50x-96y-231=0

25 x^{2} + 16 y^{2} + 50 x - 96 y - 231 = 0

(h, k) = (- 1, 3), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} + 50 x - 96 y - 231 = 0

Rewrite

25 x^{2} + 16 y^{2} + 50 x - 96 y - 231 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), b = 5, a = 4

4 x^{2} + y^{2} - 24 x + 4 y + 24 = 0

\frac{x - 3 y}{x ^{2} + y ^{2}} + 1 = 0

a^{2} + \frac{a ^{2}}{2} + \frac{b ^{2}}{2} = 26

x^{2} + y^{2} = - 12 y

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

What is 25x^2+16y^2+50x-96y-231=0 ?
The solution to 25x^2+16y^2+50x-96y-231=0 is Ellipse with (h,k)=(-1,3),a=4,b=5