What is 3x^2+8y^2+12x+48y+60=1 ?

The solution to 3x^2+8y^2+12x+48y+60=1 is Ellipse with (h,k)=(-2,-3),a= 5/(sqrt(3)),b= 5/(2sqrt(2))

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3x^2+8y^2+12x+48y+60=1

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 1

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

Solution steps

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 1

Rewrite

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 1 ) ^{2}}{4} + \frac{y ^{2}}{9} = 1

25 x^{(2)} + 16 y^{(2)} = 400

\frac{8 y}{1 + x ^{2} + y ^{2}} = 2

\frac{x ^{2}}{9} + \frac{y ^{2}}{7} = 1

\frac{y ^{2}}{a ^{2}} + \frac{x ^{2}}{b ^{2}} = 1

What is 3x^2+8y^2+12x+48y+60=1 ?
The solution to 3x^2+8y^2+12x+48y+60=1 is Ellipse with (h,k)=(-2,-3),a= 5/(sqrt(3)),b= 5/(2sqrt(2))