## samnatha 2 years ago (i) show that if the circle x^2 + y^2 + 2gx + 2fy + c = 0 touches the y- axis, then f^2 = c (ii) using the result from part (i) find the equation of the circle which contains the points (2, 3) and (2, -5) and which touches the y axis. i have done part (i) and gotten some of part (ii) but i need help finishing it please

1. satellite73

if you have part I done, the for the second part you have \[x^2+y^2+2gx+2fy+f^2=0\]

2. samnatha

i have subed the points in and got the 2 equations but now i'm not sure what to do ?

3. satellite73

replace \(x\) by 3, \(y\) by 3 and get an equation in \(f\) and \(g\) repeat with \(x=2\) and \(y=-5\)

4. satellite73

oh i didn't do it, i assumed it would be obvious but maybe not

5. samnatha

it just comes up math error ?

6. satellite73

let me see if i get it \[4+9+4g+6f+f^2=0\] or \[13+4g+6f+f^2=0\]of \[4g+6f+f^2=-13\] for the first one

7. samnatha

still math error for some reason ?

8. satellite73

\[4+25+4g-10f+f^2=0\] \[4g-10f+f^2=-29\]

9. satellite73

subtract the second equation from the first i get \[16f=16\] and so \(f=1\)

10. samnatha

[Math Processing Error] [Math Processing Error] this is what keeps coming up

11. satellite73

oh i didn't understand what you mean you mean that is what you see me write refresh your browswer

12. satellite73

for some reason your browser was not reading the latex correctly a refresh should work