What is 4x^2+25y^2+549=72x+250y ?

The solution to 4x^2+25y^2+549=72x+250y is Ellipse with (h,k)=(9,5),a=10,b=4

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4x^2+25y^2+549=72x+250y

4 x^{2} + 25 y^{2} + 549 = 72 x + 250 y

(h, k) = (9, 5), a = 10, b = 4

Solution steps

4 x^{2} + 25 y^{2} + 549 = 72 x + 250 y

Rewrite

4 x^{2} + 25 y^{2} + 549 = 72 x + 250 y

in the form of the standard ellipse equation

\frac{( x - 9 ) ^{2}}{1 0 ^{2}} + \frac{( y - 5 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (9, 5), a = 10, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (9, 5), a = 10, b = 4

y^{2} = 16 - 6 x^{2}

x^{2} + 9 y^{2} = 144

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

12 x^{2} - 22 x + 16 y^{2} = 9

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

What is 4x^2+25y^2+549=72x+250y ?
The solution to 4x^2+25y^2+549=72x+250y is Ellipse with (h,k)=(9,5),a=10,b=4