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}{( x ^{2} + y ^{2} )} = 1

7 x^{2} + 5 y^{2} = 1

4 x^{2} - 6 x + y^{2} + 2 y = - 1

x^{2} + 6 x + 9 y^{2} - 36 y + 36 = 0

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{36} = 1

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