What is 4x^2+9y^2-48x+72y-144=0 ?

The solution to 4x^2+9y^2-48x+72y-144=0 is Ellipse with (h,k)=(6,-4),a=6sqrt(3),b=4sqrt(3)

Popular >

4x^2+9y^2-48x+72y-144=0

4 x^{2} + 9 y^{2} - 48 x + 72 y - 144 = 0

(h, k) = (6, - 4), a = 63, b = 43

Solution steps

4 x^{2} + 9 y^{2} - 48 x + 72 y - 144 = 0

Rewrite

4 x^{2} + 9 y^{2} - 48 x + 72 y - 144 = 0

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{( 6 3 ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( 4 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, - 4), a = 63, b = 43

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, - 4), a = 63, b = 43

\frac{x ^{2}}{1 0 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

5 x^{2} + 20 x + 7 y^{2} + 14 y = 8

(\frac{x ^{2}}{4}) + \frac{y ^{2}}{9} = 5

(\frac{x ^{2}}{4}) + (\frac{y ^{2}}{16}) = 1

25 x^{2} + (y^{2} - 4 y) = 21

What is 4x^2+9y^2-48x+72y-144=0 ?
The solution to 4x^2+9y^2-48x+72y-144=0 is Ellipse with (h,k)=(6,-4),a=6sqrt(3),b=4sqrt(3)