What is 25x^2+16y^2+50x-64y-311=0 ?

The solution to 25x^2+16y^2+50x-64y-311=0 is Ellipse with (h,k)=(-1,2),a=4,b=5

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25x^2+16y^2+50x-64y-311=0

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

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

Solution steps

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

Rewrite

25 x^{2} + 16 y^{2} + 50 x - 64 y - 311 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

18 x^{2} + 24 x + 12 y^{2} - 12 y = 1

16 x^{2} + 25 y^{2} - 64 x - 50 y - 311 = 0

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

2 x^{2} + y^{2} - 7 = 0

x^{2} + 2 y^{2} - 8 x + 8 y = 20

What is 25x^2+16y^2+50x-64y-311=0 ?
The solution to 25x^2+16y^2+50x-64y-311=0 is Ellipse with (h,k)=(-1,2),a=4,b=5