Find the centres and radii of two circles passing through points (7,2) and (10,-1) respectively and both touches the line x=4 ?

please solve this question and tell what assumptions should be taken in this question.

Ans:
Hello Student,
Please find answer to your question below
Let the centre of 1^stcircle to be (a, b)
Then, radius of circle be:
a – 4
Circle is passing through (7, 2) & (4, b).
Equation of circle:




There should be one more data given.
Either the one centre point or one other point through wich circle is passing.
Similar equation will apply for 2^ndcircle.
Only difference is that it is passing through (10, -1).