1. ## circle

Show that the equation

5y2+3x2+19=4x−2x2−20y

represents a circle by rearranging it into the centre-radius form of the equation of a circle. State the coordinates of the center and the radius of the circle.

what is the center and what is the radius??

2. sorry the equation should be

5y^2+3x^2+19=4x-2x^2-20y

3. Originally Posted by pourcarlos
Show that the equation

5y2+3x2+19=4x−2x2−20y

represents a circle by rearranging it into the centre-radius form of the equation of a circle. State the coordinates of the center and the radius of the circle.

what is the center and what is the radius??
$\displaystyle 5y^2+3x^2+19 = 4x-2x^2-20y$

$\displaystyle 5x^2-4x+5y^2+20y = -19$

$\displaystyle x^2 - \frac{4}{5}x + y^2 + 4y = -\frac{19}{5}$

$\displaystyle x^2 - \frac{4}{5}x + \frac{4}{25} + y^2 + 4y + 4 = -\frac{19}{5} + \frac{4}{25} + 4$

$\displaystyle \left(x - \frac{2}{5}\right)^2 + (y + 2)^2 = \left(\frac{3}{5}\right)^2$

the last equation is in standard form for a circle ... look that up in your text to determine the center and radius.

4. ohhh i see, thank you!