What is 16x^2+25y^2-96x-300y+644=0 ?

The solution to 16x^2+25y^2-96x-300y+644=0 is Ellipse with (h,k)=(3,6),a=5,b=4

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16x^2+25y^2-96x-300y+644=0

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

(h, k) = (3, 6), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

Rewrite

16 x^{2} + 25 y^{2} - 96 x - 300 y + 644 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{5 ^{2}} + \frac{( y - 6 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 6), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 6), a = 5, b = 4

4 x^{2} + 36 y^{2} - 144 = 0

- \frac{6 - x}{4 - y} = - \frac{y}{- 2 - x}

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

2 - 1 = x^{2} + 3 y^{2}

- 25 x^{2} - 4 y^{2} = - 100

What is 16x^2+25y^2-96x-300y+644=0 ?
The solution to 16x^2+25y^2-96x-300y+644=0 is Ellipse with (h,k)=(3,6),a=5,b=4