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Popular >

x^2+2y^2=2x+8

Solution

x^{2} + 2 y^{2} = 2 x + 8

Solution

(h, k) = (1, 0), a = 3, b = \frac{3}{2}

Solution steps

x^{2} + 2 y^{2} = 2 x + 8

Rewrite

x^{2} + 2 y^{2} = 2 x + 8

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 0), a = 3, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 0), a = 3, b = \frac{3}{2}

Popular Examples

- 8 = 4 - 4 x^{2} - y^{2}

(x^2)/(5^2)+(y^2)/(13^2)=1

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

4x^2+9y^2+16x+18y-11=0

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

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

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

((x+3)^2}{25}+\frac{(y-1)^2)/4 =1

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{4} = 1

Frequently Asked Questions (FAQ)

What is x^2+2y^2=2x+8 ?
The solution to x^2+2y^2=2x+8 is Ellipse with (h,k)=(1,0),a=3,b= 3/(sqrt(2))