What is 1x^2+3y^2+8x+9y-14=0 ?

The solution to 1x^2+3y^2+8x+9y-14=0 is Ellipse with (h,k)=(-4,-3/2),a=(7sqrt(3))/2 ,b= 7/2

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1x^2+3y^2+8x+9y-14=0

1 x^{2} + 3 y^{2} + 8 x + 9 y - 14 = 0

(h, k) = (- 4, - \frac{3}{2}), a = \frac{7 3}{2}, b = \frac{7}{2}

Solution steps

1 \cdot x^{2} + 3 y^{2} + 8 x + 9 y - 14 = 0

Rewrite

1 x^{2} + 3 y^{2} + 8 x + 9 y - 14 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{( \frac{7 3}{2} ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, - \frac{3}{2}), a = \frac{7 3}{2}, b = \frac{7}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, - \frac{3}{2}), a = \frac{7 3}{2}, b = \frac{7}{2}

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 3

2 x^{2} + y^{2} + x + y = 0

9 x^{2} + 18 x + 25 y^{2} - 100 y = 116

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

(x^{2} + y^{2} - 16 x + 8 y + 80) = 4 x^{2} + 4 y^{2} - 16 x - 32 y + 80

What is 1x^2+3y^2+8x+9y-14=0 ?
The solution to 1x^2+3y^2+8x+9y-14=0 is Ellipse with (h,k)=(-4,-3/2),a=(7sqrt(3))/2 ,b= 7/2