What is (x3)^2+(y+2)^2=25 ?

The solution to (x3)^2+(y+2)^2=25 is Ellipse with (h,k)=(0,-2),a= 5/3 ,b=5

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(x3)^2+(y+2)^2=25

(x 3)^{2} + (y + 2)^{2} = 25

(h, k) = (0, - 2), a = \frac{5}{3}, b = 5

Solution steps

(x \cdot 3)^{2} + (y + 2)^{2} = 25

Rewrite

(x 3)^{2} + (y + 2)^{2} = 25

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{3} ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 2), a = \frac{5}{3}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), b = 5, a = \frac{5}{3}

(\frac{( y - 8 )}{40})^{2} + (\frac{( x + 10 )}{211})^{2} = 1

1 = (\frac{x}{84.5})^{2} + (\frac{y}{33.5})^{2}

2 x^{2} + 3 y^{2} = 6

4 x^{2} + 5 y^{2} + 16 x - 20 y + 16 = 0

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

What is (x3)^2+(y+2)^2=25 ?
The solution to (x3)^2+(y+2)^2=25 is Ellipse with (h,k)=(0,-2),a= 5/3 ,b=5