What is (x+2)^216+((y+2)^2)/(25)=1 ?

The solution to (x+2)^216+((y+2)^2)/(25)=1 is Ellipse with (h,k)=(-2,-2),a= 1/4 ,b=5

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(x+2)^216+((y+2)^2)/(25)=1

(x + 2)^{2} 16 + \frac{( y + 2 ) ^{2}}{25} = 1

(h, k) = (- 2, - 2), a = \frac{1}{4}, b = 5

Solution steps

(x + 2)^{2} \cdot 16 + \frac{( y + 2 ) ^{2}}{25} = 1

Rewrite

(x + 2)^{2} 16 + \frac{( y + 2 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 2), a = \frac{1}{4}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 2), b = 5, a = \frac{1}{4}

6 x^{2} + 25 y^{2} - 160 x - 300 y - 300 = 0

x^{2} + \frac{y ^{2}}{49} = 1

\frac{( x + 2 ) ^{2}}{49} + \frac{( y - 3 ) ^{2}}{4} = 1

x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

\frac{( x ^{2} )}{( 16 )} + \frac{( y ^{2} )}{( 25 )} = 1

What is (x+2)^216+((y+2)^2)/(25)=1 ?
The solution to (x+2)^216+((y+2)^2)/(25)=1 is Ellipse with (h,k)=(-2,-2),a= 1/4 ,b=5