What is 6x^2+96x+16y^2-40y=315 ?

The solution to 6x^2+96x+16y^2-40y=315 is Ellipse with (h,k)=(-8, 5/4),a=sqrt(362/3),b=(sqrt(181))/2

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6x^2+96x+16y^2-40y=315

6 x^{2} + 96 x + 16 y^{2} - 40 y = 315

(h, k) = (- 8, \frac{5}{4}), a = \frac{362}{3}, b = \frac{181}{2}

Solution steps

6 x^{2} + 96 x + 16 y^{2} - 40 y = 315

Rewrite

6 x^{2} + 96 x + 16 y^{2} - 40 y = 315

in the form of the standard ellipse equation

\frac{( x - ( - 8 ) ) ^{2}}{( \frac{362}{3} ) ^{2}} + \frac{( y - \frac{5}{4} ) ^{2}}{( \frac{181}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 8, \frac{5}{4}), a = \frac{362}{3}, b = \frac{181}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 8, \frac{5}{4}), a = \frac{362}{3}, b = \frac{181}{2}

(\frac{x - 2}{16})^{2} + (\frac{y + 3}{9})^{2} = 1

4 x^{2} + y^{2} - 16 x + 6 y + 9 = 0

x^{2} + 9 y^{2} = 18

9 x^{2} + 4 y^{2} - 18 x + 8 y = 23

1 x^{2} + 2 y^{2} = 9

What is 6x^2+96x+16y^2-40y=315 ?
The solution to 6x^2+96x+16y^2-40y=315 is Ellipse with (h,k)=(-8, 5/4),a=sqrt(362/3),b=(sqrt(181))/2