What is 2x^2+5y^2+8x-10y-27=0 ?

The solution to 2x^2+5y^2+8x-10y-27=0 is Ellipse with (h,k)=(-2,1),a=2sqrt(5),b=2sqrt(2)

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2x^2+5y^2+8x-10y-27=0

2 x^{2} + 5 y^{2} + 8 x - 10 y - 27 = 0

(h, k) = (- 2, 1), a = 25, b = 22

Solution steps

2 x^{2} + 5 y^{2} + 8 x - 10 y - 27 = 0

Rewrite

2 x^{2} + 5 y^{2} + 8 x - 10 y - 27 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 25, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), a = 25, b = 22

\frac{( x - 4 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{20} = 1

\frac{x ^{2}}{13} + \frac{y ^{2}}{9} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{18} = 1

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

\frac{( x + 1 ) ^{2}}{\frac{27}{4}} + \frac{( y - 4 ) ^{2}}{9} = 1

What is 2x^2+5y^2+8x-10y-27=0 ?
The solution to 2x^2+5y^2+8x-10y-27=0 is Ellipse with (h,k)=(-2,1),a=2sqrt(5),b=2sqrt(2)