Question

(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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

it just comes up math error ?

Answer 6

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

Answer 7

still math error for some reason ?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

refresh your browswer

Answer 12

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