What is 9x^2+25y^2-36x-50y+52=0 ?

The solution to 9x^2+25y^2-36x-50y+52=0 is Ellipse with (h,k)=(2,1),a=1,b= 3/5

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9x^2+25y^2-36x-50y+52=0

9 x^{2} + 25 y^{2} - 36 x - 50 y + 52 = 0

(h, k) = (2, 1), a = 1, b = \frac{3}{5}

Solution steps

9 x^{2} + 25 y^{2} - 36 x - 50 y + 52 = 0

Rewrite

9 x^{2} + 25 y^{2} - 36 x - 50 y + 52 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = 1, b = \frac{3}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = 1, b = \frac{3}{5}

64 x^{2} + 81 y^{2} = 5184

x^{2} + 4 y^{2} - 2 x + 4 y + 1 = 0

2 x^{2} + 24 y^{2} + 6 x + 4 y + 1 > 0

16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0

\frac{x ^{2}}{23} + \frac{y ^{2}}{19} = 1

What is 9x^2+25y^2-36x-50y+52=0 ?
The solution to 9x^2+25y^2-36x-50y+52=0 is Ellipse with (h,k)=(2,1),a=1,b= 3/5