What is ((x-4)^2)/5+((y-6)^2)/9 =1 ?

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

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((x-4)^2)/5+((y-6)^2)/9 =1

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 6 ) ^{2}}{9} = 1

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

Solution steps

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 6 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 6 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(\frac{( x + 2 ) ^{2}}{25}) + (\frac{( y - 1 ) ^{2}}{169}) = 1

5 y^{2} + 4 x^{2} = \frac{5}{4}

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

\frac{( x - 4 ) ^{2}}{12} + \frac{( y + 3 ) ^{2}}{16} = 1

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

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