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

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

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

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

(h, k) = (4, - 6), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 6), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 6), a = 3, b = 2

9 x^{2} + 4 y^{2} + 18 x + 32 y + 37 = 0

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

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

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

\frac{( x - 1 ) ^{2}}{7 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

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