What is x^2+9y^2-2x+72y+136=0 ?

The solution to x^2+9y^2-2x+72y+136=0 is Ellipse with (h,k)=(1,-4),a=3,b=1

Popular >

x^2+9y^2-2x+72y+136=0

x^{2} + 9 y^{2} - 2 x + 72 y + 136 = 0

(h, k) = (1, - 4), a = 3, b = 1

Solution steps

x^{2} + 9 y^{2} - 2 x + 72 y + 136 = 0

Rewrite

x^{2} + 9 y^{2} - 2 x + 72 y + 136 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 4), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 4), a = 3, b = 1

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

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

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{26}{16}} = 1

y^{2} = 1 - \frac{x ^{2}}{a ^{2}}

What is x^2+9y^2-2x+72y+136=0 ?
The solution to x^2+9y^2-2x+72y+136=0 is Ellipse with (h,k)=(1,-4),a=3,b=1