What is 6.25x^2+16y^2-12.5x+64y-29.75=0 ?

The solution to 6.25x^2+16y^2-12.5x+64y-29.75=0 is Ellipse with (h,k)=(1,-2),a=4,b=2.5

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6.25x^2+16y^2-12.5x+64y-29.75=0

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

(h, k) = (1, - 2), a = 4, b = 2.5

Solution steps

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

Rewrite

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 4, b = 2.5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = 4, b = 2.5

4 x^{2} + 25 y^{2} + 4 x - 120 y + 45 = 0

4 x^{2} + y^{2} = 72

64 x^{2} + 25 y^{2} - 16 x - 16 y - 648 = 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

3 x^{2} + 4 y^{2} = 12

What is 6.25x^2+16y^2-12.5x+64y-29.75=0 ?
The solution to 6.25x^2+16y^2-12.5x+64y-29.75=0 is Ellipse with (h,k)=(1,-2),a=4,b=2.5