What is 36(x+2)^2+(y-4)^2=72 ?

The solution to 36(x+2)^2+(y-4)^2=72 is Ellipse with (h,k)=(-2,4),a=sqrt(2),b=6sqrt(2)

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36(x+2)^2+(y-4)^2=72

36 (x + 2)^{2} + (y - 4)^{2} = 72

(h, k) = (- 2, 4), a = 2, b = 62

Solution steps

36 (x + 2)^{2} + (y - 4)^{2} = 72

Rewrite

36 (x + 2)^{2} + (y - 4)^{2} = 72

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 4), a = 2, b = 62

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 4), b = 62, a = 2

\frac{( x - 2 ) ^{2}}{4} + \frac{y ^{2}}{33} = 1

\frac{( x + 1 ) ^{2}}{21} + \frac{( y + 5 ) ^{2}}{25} = 1

4 x^{2} + 3 y^{2} = 7

25 x^{2} + 4 y^{2} - 250 x - 16 y = - 541

x^{2} + \frac{z ^{2}}{225} = 1

What is 36(x+2)^2+(y-4)^2=72 ?
The solution to 36(x+2)^2+(y-4)^2=72 is Ellipse with (h,k)=(-2,4),a=sqrt(2),b=6sqrt(2)