What is 2x^2+3y^2+12x=10 ?

The solution to 2x^2+3y^2+12x=10 is Ellipse with (h,k)=(-3,0),a=sqrt(14),b=(2sqrt(7))/(sqrt(3))

Popular >

2x^2+3y^2+12x=10

2 x^{2} + 3 y^{2} + 12 x = 10

(h, k) = (- 3, 0), a = 14, b = \frac{2 7}{3}

Solution steps

2 x^{2} + 3 y^{2} + 12 x = 10

Rewrite

2 x^{2} + 3 y^{2} + 12 x = 10

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 14 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2 7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 0), a = 14, b = \frac{2 7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 0), a = 14, b = \frac{2 7}{3}

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

\frac{( x + 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{16} = 1

18 x^{2} - 72 x + 4 y^{2} + 4 y + 37 = 0

6 (x + 1)^{2} + 2 (y - 1)^{2} = 72

\frac{( x - \frac{5}{2} ) ^{2}}{9} + \frac{y ^{2}}{49} = 1

What is 2x^2+3y^2+12x=10 ?
The solution to 2x^2+3y^2+12x=10 is Ellipse with (h,k)=(-3,0),a=sqrt(14),b=(2sqrt(7))/(sqrt(3))