What is 9x^2+25y^2-36x-189=0 ?

The solution to 9x^2+25y^2-36x-189=0 is Ellipse with (h,k)=(2,0),a=5,b=3

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9x^2+25y^2-36x-189=0

9 x^{2} + 25 y^{2} - 36 x - 189 = 0

(h, k) = (2, 0), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} - 36 x - 189 = 0

Rewrite

9 x^{2} + 25 y^{2} - 36 x - 189 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{5 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 0), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 5, b = 3

9 x^{2} + 25 y^{2} - 18 x - 150 y + 9 = 0

2 x^{2} + 3 y^{2} + 8 x + 9 y - 10 = 0

2 x^{2} + 3 y^{2} - 8 x + 6 y + 5 = 0

3 x^{2} + y^{2} + 2 x - 6 y - 3 = 0

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

What is 9x^2+25y^2-36x-189=0 ?
The solution to 9x^2+25y^2-36x-189=0 is Ellipse with (h,k)=(2,0),a=5,b=3