What is 11x^2+5y^2+110x-20y+240=0 ?

The solution to 11x^2+5y^2+110x-20y+240=0 is Ellipse with (h,k)=(-5,2),a=sqrt(5),b=sqrt(11)

Popular >

11x^2+5y^2+110x-20y+240=0

11 x^{2} + 5 y^{2} + 110 x - 20 y + 240 = 0

(h, k) = (- 5, 2), a = 5, b = 11

Solution steps

11 x^{2} + 5 y^{2} + 110 x - 20 y + 240 = 0

Rewrite

11 x^{2} + 5 y^{2} + 110 x - 20 y + 240 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 5 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 11 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 2), a = 5, b = 11

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 5, 2), b = 11, a = 5

\frac{x ^{2}}{cosh ^{2} ( β )} + \frac{y ^{2}}{sinh ^{2} ( β )} = 1

4 x^{2} = 36 - 9 y^{2}

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{16} = 1

25 x^{2} + 16 y^{2} + 100 x - 96 y - 154 = 0

\frac{( x + 1 ) ^{2}}{25} + \frac{( y + 5 ) ^{2}}{16} = 1

What is 11x^2+5y^2+110x-20y+240=0 ?
The solution to 11x^2+5y^2+110x-20y+240=0 is Ellipse with (h,k)=(-5,2),a=sqrt(5),b=sqrt(11)