What is 6.25x^2+16y^2-1.25x+64y-29.75=0 ?

The solution to 6.25x^2+16y^2-1.25x+64y-29.75=0 is Ellipse with (h,k)=(0.1,-2),a=3.87427…,b=2.42142…

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6.25x^2+16y^2-1.25x+64y-29.75=0

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

(h, k) = (0.1, - 2), a = 3.87427 \dots, b = 2.42142 \dots

Solution steps

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

Rewrite

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

in the form of the standard ellipse equation

\frac{( x - 0.1 ) ^{2}}{3.87427 \dots ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{2.42142 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0.1, - 2), a = 3.87427 \dots, b = 2.42142 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0.1, - 2), a = 3.87427 \dots, b = 2.42142 \dots

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{5.9 1 ^{2}} = 1

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

\frac{( ( x + 0 ) ^{2} )}{40} + \frac{( ( y + 0 ) ^{2} )}{32} = 1

\frac{( x - 5 ) ^{2}}{16} + \frac{( y + 15 ) ^{2}}{25} = 1

What is 6.25x^2+16y^2-1.25x+64y-29.75=0 ?
The solution to 6.25x^2+16y^2-1.25x+64y-29.75=0 is Ellipse with (h,k)=(0.1,-2),a=3.87427…,b=2.42142…