What is 12x^2+16y^2-120x+64y+172=0 ?

The solution to 12x^2+16y^2-120x+64y+172=0 is Ellipse with (h,k)=(5,-2),a=4,b=2sqrt(3)

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12x^2+16y^2-120x+64y+172=0

12 x^{2} + 16 y^{2} - 120 x + 64 y + 172 = 0

(h, k) = (5, - 2), a = 4, b = 23

Solution steps

12 x^{2} + 16 y^{2} - 120 x + 64 y + 172 = 0

Rewrite

12 x^{2} + 16 y^{2} - 120 x + 64 y + 172 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 2), a = 4, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 2), a = 4, b = 23

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

x^{2} + y^{2} - 10 y = 0

16 x^{2} + 25 y^{2} - 64 x + 150 y - 111 = 0

25 x^{2} + 9 y^{2} - 225 = 0

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

What is 12x^2+16y^2-120x+64y+172=0 ?
The solution to 12x^2+16y^2-120x+64y+172=0 is Ellipse with (h,k)=(5,-2),a=4,b=2sqrt(3)