What is 15x^2+12y^2+30x-24y=150 ?

The solution to 15x^2+12y^2+30x-24y=150 is Ellipse with (h,k)=(-1,1),a=sqrt(59/5),b=(sqrt(59))/2

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15x^2+12y^2+30x-24y=150

15 x^{2} + 12 y^{2} + 30 x - 24 y = 150

(h, k) = (- 1, 1), a = \frac{59}{5}, b = \frac{59}{2}

Solution steps

15 x^{2} + 12 y^{2} + 30 x - 24 y = 150

Rewrite

15 x^{2} + 12 y^{2} + 30 x - 24 y = 150

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{59}{5} ) ^{2}} + \frac{( y - 1 ) ^{2}}{( \frac{59}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = \frac{59}{5}, b = \frac{59}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = \frac{59}{2}, a = \frac{59}{5}

2 x^{2} + 5 y^{2} - 4 x + y - 6 = 0

30 x^{2} + 9 y^{2} = 225

3 x^{2} + 8 y^{2} = 1

\frac{( x - 2.63 ) ^{2}}{1.34} + \frac{y ^{2}}{3.22} - 1 = 1

4 x^{2} + y^{2} - 32 x - 80 = 0

What is 15x^2+12y^2+30x-24y=150 ?
The solution to 15x^2+12y^2+30x-24y=150 is Ellipse with (h,k)=(-1,1),a=sqrt(59/5),b=(sqrt(59))/2