What is ((x+5)^2)/9+((y-3)^2)/(25)=1 ?

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

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((x+5)^2)/9+((y-3)^2)/(25)=1

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

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

Solution steps

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( ( x + 0 ) ^{2} )}{100} + \frac{( ( y + 0 ) ^{2} )}{49} = 1

2 x^{2} + 3 y^{2} + 9 x + 10 y - 3 = 0

\frac{( x - 9 ) ^{2}}{64} + \frac{( y + 2 ) ^{2}}{25} = 1

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

(3 p + 2 q) 2 = 9 p^{2} + 4 q^{2}

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