What is 9x^2+16y^2+54x+64y+1=0 ?

The solution to 9x^2+16y^2+54x+64y+1=0 is Ellipse with (h,k)=(-3,-2),a=4,b=3

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9x^2+16y^2+54x+64y+1=0

9 x^{2} + 16 y^{2} + 54 x + 64 y + 1 = 0

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

Solution steps

9 x^{2} + 16 y^{2} + 54 x + 64 y + 1 = 0

Rewrite

9 x^{2} + 16 y^{2} + 54 x + 64 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x + 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{16} = 1

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

\frac{1}{2} (3 x^{2} + y^{2}) - 2 (x - y) = 0

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

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 11

What is 9x^2+16y^2+54x+64y+1=0 ?
The solution to 9x^2+16y^2+54x+64y+1=0 is Ellipse with (h,k)=(-3,-2),a=4,b=3