What is 25x^2+16y^2-150x+64y=111 ?

The solution to 25x^2+16y^2-150x+64y=111 is Ellipse with (h,k)=(3,-2),a=4,b=5

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25x^2+16y^2-150x+64y=111

25 x^{2} + 16 y^{2} - 150 x + 64 y = 111

(h, k) = (3, - 2), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} - 150 x + 64 y = 111

Rewrite

25 x^{2} + 16 y^{2} - 150 x + 64 y = 111

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), b = 5, a = 4

\frac{x ^{2}}{25} + \frac{y ^{2}}{1} = 1

\frac{x ^{2}}{2 7 ^{2}} + \frac{y ^{2}}{2 5 ^{2}} = 1

1 - x^{2} = \frac{y ^{2}}{4}

\frac{2 x}{x ^{2} + 2 y ^{2}} = 2

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

What is 25x^2+16y^2-150x+64y=111 ?
The solution to 25x^2+16y^2-150x+64y=111 is Ellipse with (h,k)=(3,-2),a=4,b=5