Circles

[hexed iron]

show that (x-3)^2 + (y-5)^2 =4 touches the circle x^2 + (y-1)^2 = 9?

I don't even know how to approach this one, I know I should use simultaneous equation substitution method and then discriminant to see how many points of intersection, but I can't even substitute them?

[vernal willow]

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[dark umbra]

Let's assume for the sake of argument that the circles are tangent. If that's the case, how would you find the point of tangency?

[formal nexus]

you have three senses in math

1. symbolic
2. visual
3. verbal
   now you see equations, and you're lost
   so you wanna switch to another way of thinking

[hexed iron]

is this about the distance between the centre of both circles = sum of the radii of both circles? (Aka, external touching of the circles)?

[hexed iron]

Visual maybe, plotting both circles on a graph?

[formal nexus]

a sketch with a qualitative description in mind would do

[hexed iron]

ahh i see thank you 🙂