What is ((x-7)^2)/(64)+((y-6)^2)/(36)=1 ?

The solution to ((x-7)^2)/(64)+((y-6)^2)/(36)=1 is Ellipse with (h,k)=(7,6),a=8,b=6

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((x-7)^2)/(64)+((y-6)^2)/(36)=1

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

(h, k) = (7, 6), a = 8, b = 6

Solution steps

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

Rewrite

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{8 ^{2}} + \frac{( y - 6 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, 6), a = 8, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, 6), a = 8, b = 6

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

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{26}{16}} = 1

y^{2} = 1 - \frac{x ^{2}}{a ^{2}}

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

4 x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

What is ((x-7)^2)/(64)+((y-6)^2)/(36)=1 ?
The solution to ((x-7)^2)/(64)+((y-6)^2)/(36)=1 is Ellipse with (h,k)=(7,6),a=8,b=6