What is 9x^2-72x+y^2+10y+160=0 ?

The solution to 9x^2-72x+y^2+10y+160=0 is Ellipse with (h,k)=(4,-5),a=1,b=3

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9x^2-72x+y^2+10y+160=0

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

(h, k) = (4, - 5), a = 1, b = 3

Solution steps

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

Rewrite

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 5), a = 1, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 5), b = 3, a = 1

\frac{x ^{2}}{3} + \frac{y ^{2}}{6} = 1

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

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

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

(\frac{x ^{2}}{64}) + (\frac{y ^{2}}{25}) = 1

What is 9x^2-72x+y^2+10y+160=0 ?
The solution to 9x^2-72x+y^2+10y+160=0 is Ellipse with (h,k)=(4,-5),a=1,b=3