What is 36x^2+288x+64y^2-256y=1472 ?

The solution to 36x^2+288x+64y^2-256y=1472 is Ellipse with (h,k)=(-4,2),a=8,b=6

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36x^2+288x+64y^2-256y=1472

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

(h, k) = (- 4, 2), a = 8, b = 6

Solution steps

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

Rewrite

36 x^{2} + 288 x + 64 y^{2} - 256 y = 1472

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{8 ^{2}} + \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 2), a = 8, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 2), a = 8, b = 6

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

y^{2} - 4 y - 8 x - 12 = 0

f (x) = x^{2} - 5 x

3 x^{2} + 2 y = 26

y^{2} = - 2 x

What is 36x^2+288x+64y^2-256y=1472 ?
The solution to 36x^2+288x+64y^2-256y=1472 is Ellipse with (h,k)=(-4,2),a=8,b=6