What is 25x^2+9y^2-150x-36y+36=0 ?

The solution to 25x^2+9y^2-150x-36y+36=0 is Ellipse with (h,k)=(3,2),a=3,b=5

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25x^2+9y^2-150x-36y+36=0

25 x^{2} + 9 y^{2} - 150 x - 36 y + 36 = 0

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

Solution steps

25 x^{2} + 9 y^{2} - 150 x - 36 y + 36 = 0

Rewrite

25 x^{2} + 9 y^{2} - 150 x - 36 y + 36 = 0

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

100 y^{2} + 64 x^{2} = 6400

(x - 4)^{2} + \frac{( y - 2 ) ^{2}}{9} = 1

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

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

What is 25x^2+9y^2-150x-36y+36=0 ?
The solution to 25x^2+9y^2-150x-36y+36=0 is Ellipse with (h,k)=(3,2),a=3,b=5