What is 2.4x^2+4y^2+40x-32y-5=0 ?

The solution to 2.4x^2+4y^2+40x-32y-5=0 is Ellipse with (h,k)=(-8.33333…,4),a=9.90931…,b=7.67571…

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2.4x^2+4y^2+40x-32y-5=0

2.4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

(h, k) = (- 8.33333 \dots, 4), a = 9.90931 \dots, b = 7.67571 \dots

Solution steps

2.4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

Rewrite

2.4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 8.33333 \dots ) ) ^{2}}{9.90931 \dots ^{2}} + \frac{( y - 4 ) ^{2}}{7.67571 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 8.33333 \dots, 4), a = 9.90931 \dots, b = 7.67571 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 8.33333 \dots, 4), a = 9.90931 \dots, b = 7.67571 \dots

25 x^{2} + 16 y^{2} + 100 x - 32 y - 284 = 0

x^{2} + 3 y^{2} - 3 x - 5 y = 0

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

\frac{x ^{2}}{1} + \frac{y ^{2}}{5} = 1

4 x^{2} + y^{2} + 56 = 4 y - 56 x

What is 2.4x^2+4y^2+40x-32y-5=0 ?
The solution to 2.4x^2+4y^2+40x-32y-5=0 is Ellipse with (h,k)=(-8.33333…,4),a=9.90931…,b=7.67571…