What is 4x^2+24x+36+36y^2-360y+756=0 ?

The solution to 4x^2+24x+36+36y^2-360y+756=0 is Ellipse with (h,k)=(-3,5),a=6,b=2

Popular >

4x^2+24x+36+36y^2-360y+756=0

4 x^{2} + 24 x + 36 + 36 y^{2} - 360 y + 756 = 0

(h, k) = (- 3, 5), a = 6, b = 2

Solution steps

4 x^{2} + 24 x + 36 + 36 y^{2} - 360 y + 756 = 0

Rewrite

4 x^{2} + 24 x + 36 + 36 y^{2} - 360 y + 756 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{6 ^{2}} + \frac{( y - 5 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 5), a = 6, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 5), a = 6, b = 2

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

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

9 x^{2} + 36 y^{2} - 54 x + 72 y - 207 = 0

4 x^{2} + y^{2} - 48 x + 4 y + 48 = 0

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

What is 4x^2+24x+36+36y^2-360y+756=0 ?
The solution to 4x^2+24x+36+36y^2-360y+756=0 is Ellipse with (h,k)=(-3,5),a=6,b=2