Equations of Circles Qn

knt SG

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 SG

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 SG

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