What is (x^2+12x+36)/(100)+(y^2)/(64)=1 ?

The solution to (x^2+12x+36)/(100)+(y^2)/(64)=1 is Ellipse with (h,k)=(-6,0),a=10,b=8

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(x^2+12x+36)/(100)+(y^2)/(64)=1

\frac{x ^{2} + 12 x + 36}{100} + \frac{y ^{2}}{64} = 1

(h, k) = (- 6, 0), a = 10, b = 8

Solution steps

\frac{x ^{2} + 12 x + 36}{100} + \frac{y ^{2}}{64} = 1

Rewrite

\frac{x ^{2} + 12 x + 36}{100} + \frac{y ^{2}}{64} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 0 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 0), a = 10, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 0), a = 10, b = 8

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

1 = 4 x^{2} + 2 y^{2}

x^{2} + 2 y^{2} - 6 y = 18

\frac{( x - 4 ) ^{2}}{32} + \frac{( y - 3 ) ^{2}}{36} = 1

\frac{( x ^{2} )}{63500} + \frac{( y ^{2} )}{50900} = 1

What is (x^2+12x+36)/(100)+(y^2)/(64)=1 ?
The solution to (x^2+12x+36)/(100)+(y^2)/(64)=1 is Ellipse with (h,k)=(-6,0),a=10,b=8