What is 9x^2+25y^2-36x+50y-164=0 ?

The solution to 9x^2+25y^2-36x+50y-164=0 is Ellipse with (h,k)=(2,-1),a=5,b=3

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9x^2+25y^2-36x+50y-164=0

9 x^{2} + 25 y^{2} - 36 x + 50 y - 164 = 0

(h, k) = (2, - 1), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} - 36 x + 50 y - 164 = 0

Rewrite

9 x^{2} + 25 y^{2} - 36 x + 50 y - 164 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), a = 5, b = 3

\frac{( x - 5 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{4} - 1 = 0

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

4 x^{2} + 9 y^{2} - 8 x - 36 + 4 = 0

x^{2} + 4 y^{2} - 10 x - 40 y + 121 = 0

2 x^{2} + 7 y^{2} - 14 = 0

What is 9x^2+25y^2-36x+50y-164=0 ?
The solution to 9x^2+25y^2-36x+50y-164=0 is Ellipse with (h,k)=(2,-1),a=5,b=3