What is ((x+4)^2)/9+((y-6)^2)/(25)=1 ?

The solution to ((x+4)^2)/9+((y-6)^2)/(25)=1 is Ellipse with (h,k)=(-4,6),a=3,b=5

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((x+4)^2)/9+((y-6)^2)/(25)=1

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

(h, k) = (- 4, 6), a = 3, b = 5

Solution steps

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

Rewrite

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{3 ^{2}} + \frac{( y - 6 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, 6), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 4, 6), b = 5, a = 3

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

4 y^{2} + 16 x^{2} - 36 x - 20 y + 36 = 0

\frac{x ^{2}}{25} + \frac{y ^{2}}{76} = 1

x^{2} + 4 y^{2} = - 4 x

2 y^{2} = 4 - 5 x^{2}

What is ((x+4)^2)/9+((y-6)^2)/(25)=1 ?
The solution to ((x+4)^2)/9+((y-6)^2)/(25)=1 is Ellipse with (h,k)=(-4,6),a=3,b=5