What is 3x^2+4y^2+24x-16y+52=0 ?

The solution to 3x^2+4y^2+24x-16y+52=0 is Ellipse with (h,k)=(-4,2),a=2,b=sqrt(3)

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3x^2+4y^2+24x-16y+52=0

3 x^{2} + 4 y^{2} + 24 x - 16 y + 52 = 0

(h, k) = (- 4, 2), a = 2, b = 3

Solution steps

3 x^{2} + 4 y^{2} + 24 x - 16 y + 52 = 0

Rewrite

3 x^{2} + 4 y^{2} + 24 x - 16 y + 52 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 2), a = 2, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 2), a = 2, b = 3

What is 3x^2+4y^2+24x-16y+52=0 ?
The solution to 3x^2+4y^2+24x-16y+52=0 is Ellipse with (h,k)=(-4,2),a=2,b=sqrt(3)