Two circle problems - Math Central

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Question from shahad, a student:

question 1
find an equation for the circle through the point (0,0) and (6,0) that a tangent to the line y=-1
question 2
find an equation for the circle through the point (0,0) and (17,7) whose center lies on the line 12x-5y=0

Hi Shahad,

I'll give you some help with problem 1, a similar approach works with problem 2.

In problem 1 the center $C$ of the circle must be on the line $x = 3.$ Thus $C$ has coordinates $(3, k)$ for some number $k.$

circle

Thus the distance from $C$ to $(0, 0)$ must equal the distance from $C$ to $(3, -1).$

Solve for $k.$

Penny

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