What is x^2+5y^2+6x-40y-167=0 ?

The solution to x^2+5y^2+6x-40y-167=0 is Ellipse with (h,k)=(-3,4),a=16,b=(16)/(sqrt(5))

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x^2+5y^2+6x-40y-167=0

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

(h, k) = (- 3, 4), a = 16, b = \frac{16}{5}

Solution steps

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

Rewrite

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{1 6 ^{2}} + \frac{( y - 4 ) ^{2}}{( \frac{16}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 4), a = 16, b = \frac{16}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 4), a = 16, b = \frac{16}{5}

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

\frac{( x - 2 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{9} = 1

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

\frac{( x + 1 ) ^{2}}{28} + \frac{( y + 5 ) ^{2}}{23} = 1

What is x^2+5y^2+6x-40y-167=0 ?
The solution to x^2+5y^2+6x-40y-167=0 is Ellipse with (h,k)=(-3,4),a=16,b=(16)/(sqrt(5))