What is x^2+2y^2-3x+4y+0.25=0 ?

The solution to x^2+2y^2-3x+4y+0.25=0 is Ellipse with (h,k)=(3/2 ,-1),a=2,b=sqrt(2)

Popular >

x^2+2y^2-3x+4y+0.25=0

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

(h, k) = (\frac{3}{2}, - 1), a = 2, b = 2

Solution steps

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

Rewrite

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, - 1), a = 2, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, - 1), a = 2, b = 2

2 x^{2} + y^{2} = 225

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{7} = 1

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{16} = 1

4 x^{2} + 9 y^{2} = 40

2 x^{2} + 2 y^{2} + 4 y = 0

What is x^2+2y^2-3x+4y+0.25=0 ?
The solution to x^2+2y^2-3x+4y+0.25=0 is Ellipse with (h,k)=(3/2 ,-1),a=2,b=sqrt(2)