What is 25x^2+16y^2+150x-128y-1119=0 ?

The solution to 25x^2+16y^2+150x-128y-1119=0 is Ellipse with (h,k)=(-3,4),a=8,b=10

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25x^2+16y^2+150x-128y-1119=0

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

(h, k) = (- 3, 4), a = 8, b = 10

Solution steps

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

Rewrite

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{8 ^{2}} + \frac{( y - 4 ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 4), a = 8, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 4), b = 10, a = 8

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{16} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{49} = 1

3 x^{2} + 2 y^{2} = 5 x + y

36 x^{2} + y^{2} - 8 y = 0

- x^{2} - y^{2} = 1

What is 25x^2+16y^2+150x-128y-1119=0 ?
The solution to 25x^2+16y^2+150x-128y-1119=0 is Ellipse with (h,k)=(-3,4),a=8,b=10