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

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

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

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

(h, k) = (4, - 9), a = 1, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 9 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 9), a = 1, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 9), b = 3, a = 1

x, 2^{2} = h (x)^{2} + (\frac{x}{2})^{2}

4 x^{2} + y^{2} \leq 17

0.5 = 4 x^{2} + y^{2}

\frac{x ^{2}}{9} + y^{2} > 9

\frac{( x + 8 ) ^{2}}{20} + \frac{( y + 36 ) ^{2}}{36} = 1

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