What is 25x^2+9y^2-150x-36y=-36 ?

The solution to 25x^2+9y^2-150x-36y=-36 is Ellipse with (h,k)=(3,2),a=3,b=5

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25x^2+9y^2-150x-36y=-36

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

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

Solution steps

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

Rewrite

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 2), a = 3, 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 = 3

\frac{( x - 23 ) ^{2}}{841} + \frac{( y + 28 ) ^{2}}{484} = 1

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

(x - 7)^{2} + 6 y^{2} + 12 y = 0

(\frac{x + 2}{4})^{2} + (\frac{y - 3}{16})^{2} = 1

4 x^{2} + 9 y^{2} = 2 x

What is 25x^2+9y^2-150x-36y=-36 ?
The solution to 25x^2+9y^2-150x-36y=-36 is Ellipse with (h,k)=(3,2),a=3,b=5