What is 5u^2-4*u+v^2+2*v=0 ?

The solution to 5u^2-4*u+v^2+2*v=0 is Ellipse with (h,k)=(2/5 ,-1),a= 3/5 ,b= 3/(sqrt(5))

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5u^2-4u+v^2+2v=0

5 u^{2} - 4 \cdot u + v^{2} + 2 \cdot v = 0

(h, k) = (\frac{2}{5}, - 1), a = \frac{3}{5}, b = \frac{3}{5}

Solution steps

5 u^{2} - 4 u + v^{2} + 2 v = 0

Rewrite

5 u^{2} - 4 \cdot u + v^{2} + 2 \cdot v = 0

in the form of the standard ellipse equation

\frac{( u - \frac{2}{5} ) ^{2}}{( \frac{3}{5} ) ^{2}} + \frac{( v - ( - 1 ) ) ^{2}}{( \frac{3}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{2}{5}, - 1), a = \frac{3}{5}, b = \frac{3}{5}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{2}{5}, - 1), b = \frac{3}{5}, a = \frac{3}{5}

3 x^{2} + 2 y^{2} - 6 x - 12 y + 15 = 0

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

4 x^{2} + 7 y^{2} - 140 = 0

x^{2} + 5 y^{2} - 30 y + 25 = 0

3 x^{2} + 9 y^{2} - 6 x - 7 y - 8 = 0

What is 5u^2-4*u+v^2+2*v=0 ?
The solution to 5u^2-4*u+v^2+2*v=0 is Ellipse with (h,k)=(2/5 ,-1),a= 3/5 ,b= 3/(sqrt(5))