What is 25x^2+350x+16y^2+96y-2231=0 ?

The solution to 25x^2+350x+16y^2+96y-2231=0 is Ellipse with (h,k)=(-7,-3),a=12,b=15

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25x^2+350x+16y^2+96y-2231=0

25 x^{2} + 350 x + 16 y^{2} + 96 y - 2231 = 0

(h, k) = (- 7, - 3), a = 12, b = 15

Solution steps

25 x^{2} + 350 x + 16 y^{2} + 96 y - 2231 = 0

Rewrite

25 x^{2} + 350 x + 16 y^{2} + 96 y - 2231 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 7 ) ) ^{2}}{1 2 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{1 5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 7, - 3), a = 12, b = 15

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 7, - 3), b = 15, a = 12

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{25} = 1

64 y^{2} - 512 y - (- x^{2} - 16 x + 105) = 0

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

4 x^{2} + 36 y^{2} - 144 = 0

- \frac{6 - x}{4 - y} = - \frac{y}{- 2 - x}

What is 25x^2+350x+16y^2+96y-2231=0 ?
The solution to 25x^2+350x+16y^2+96y-2231=0 is Ellipse with (h,k)=(-7,-3),a=12,b=15