What is x^2+30x+12y^2=0 ?

The solution to x^2+30x+12y^2=0 is Ellipse with (h,k)=(-15,0),a=15,b=(5sqrt(3))/2

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x^2+30x+12y^2=0

x^{2} + 30 x + 12 y^{2} = 0

(h, k) = (- 15, 0), a = 15, b = \frac{5 3}{2}

Solution steps

x^{2} + 30 x + 12 y^{2} = 0

Rewrite

x^{2} + 30 x + 12 y^{2} = 0

in the form of the standard ellipse equation

\frac{( x - ( - 15 ) ) ^{2}}{1 5 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5 3}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 15, 0), a = 15, b = \frac{5 3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 15, 0), a = 15, b = \frac{5 3}{2}

9 x^{2} + 14 y^{2} = 126

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1

x^{2} + \frac{y ^{2}}{12} = 1

25 X^{2} + 4 Y^{2} - 250 X - 16 Y + 541 = 0

(\frac{x ^{2}}{169}) + (\frac{y ^{2}}{144}) = 1

What is x^2+30x+12y^2=0 ?
The solution to x^2+30x+12y^2=0 is Ellipse with (h,k)=(-15,0),a=15,b=(5sqrt(3))/2