What is 3x^2+12x+4y^2-40y+100=0 ?

The solution to 3x^2+12x+4y^2-40y+100=0 is Ellipse with (h,k)=(-2,5),a=2,b=sqrt(3)

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3x^2+12x+4y^2-40y+100=0

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

(h, k) = (- 2, 5), a = 2, b = 3

Solution steps

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

Rewrite

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 5), a = 2, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 5), a = 2, b = 3

(x + 2)^{2} + (y - 4)^{2} = 25

9 x^{2} - 4 y^{2} - 72 x = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{64} = 1

9 x^{2} - 16 y^{2} = 144

2 x^{2} + 2 y^{2} - 12 x + 8 y - 24 = 0

What is 3x^2+12x+4y^2-40y+100=0 ?
The solution to 3x^2+12x+4y^2-40y+100=0 is Ellipse with (h,k)=(-2,5),a=2,b=sqrt(3)