What is 36x^2+64y^2+180x-256y-95=0 ?

The solution to 36x^2+64y^2+180x-256y-95=0 is Ellipse with (h,k)=(-5/2 ,2),a=4,b=3

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36x^2+64y^2+180x-256y-95=0

36 x^{2} + 64 y^{2} + 180 x - 256 y - 95 = 0

(h, k) = (- \frac{5}{2}, 2), a = 4, b = 3

Solution steps

36 x^{2} + 64 y^{2} + 180 x - 256 y - 95 = 0

Rewrite

36 x^{2} + 64 y^{2} + 180 x - 256 y - 95 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- \frac{5}{2}, 2), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{5}{2}, 2), a = 4, b = 3

25 x^{2} + 9 y^{2} = 2245

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

9 x^{2} + 27 y^{2} - 6 x - 108 y + 82 = 0

\frac{x ^{2}}{2} + \frac{y ^{2}}{7} = 1

2 (x^{2} + 3 x + 2.25) + y (3 y - 1 + 1) = - 4 + 4.5 + 1

What is 36x^2+64y^2+180x-256y-95=0 ?
The solution to 36x^2+64y^2+180x-256y-95=0 is Ellipse with (h,k)=(-5/2 ,2),a=4,b=3