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

4 x^{2} - 24 x + 36 y^{2} - 360 y + 864 = 0

3 (x - 1)^{2} + (y - 3)^{2} = 27

4 x^{2} + y^{2} + 4 x + 2 y + 1 = 0

\frac{( x - 1 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{1}{x + y i} + \frac{1}{x - y i} < - 1

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