What is 3x^2+5y^2-12x+30y=-42 ?

The solution to 3x^2+5y^2-12x+30y=-42 is Ellipse with (h,k)=(2,-3),a=sqrt(5),b=sqrt(3)

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3x^2+5y^2-12x+30y=-42

3 x^{2} + 5 y^{2} - 12 x + 30 y = - 42

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

Solution steps

3 x^{2} + 5 y^{2} - 12 x + 30 y = - 42

Rewrite

3 x^{2} + 5 y^{2} - 12 x + 30 y = - 42

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + 3 y^{2} = 12

4 x^{2} + y^{2} - 16 x + 15 = 0

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1

4 x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

What is 3x^2+5y^2-12x+30y=-42 ?
The solution to 3x^2+5y^2-12x+30y=-42 is Ellipse with (h,k)=(2,-3),a=sqrt(5),b=sqrt(3)