Equations of Circles Qn

• knt

  14 Oct 09, 16:31

  Hi all

  I would appreciate it if someone could help me solve the following question:

  Find the possible equations of the circles that touch both axis and passes through the point A (-8,1).

  Thanks so much!

• TenSaru

  14 Oct 09, 20:27

  since circle touch (which probably means meeting it once, otherwise there are too many possibilities) the 2 axes,

  coordinates of centre is (-a,a) and radius of circle is a <<< circle is in "2nd quadrant" as it passes through (-8,1) and doesn't cut the axes; For it to touch both axes, radius is the perpendicular distance from the centre of circle to axes >>>

  (x+a)²+(y-a)²=a²

  sub (-8, 1), (a-8)²+(1-a)²=a²

  (a²-16a+64) + (a²-2a+1) = a²

  a²-18a+65 = 0

  a=13 or 5

  so equations are (x+13)² + (y-13)² = 169

  and (x+5)² + (y-5)² = 25

   

  I got a feeling there's a mistake somewhere though...

• knt

  15 Oct 09, 09:16

  Hi TenSaru

  Thanks so much!! :)))  Why do you feel that there is a mistake? Is it the question?

  Do you know where i can get hold of challenging equations of circle questions and notes? It is a new topic so not many books have it.

  Have a great day!

  Cheers