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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.

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.

Grade:12th pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below
Let the centre of 1stcircle to be (a, b)
Then, radius of circle be:
a – 4
Circle is passing through (7, 2) & (4, b).
Equation of circle:
(x-a)^{2} + (y-b)^{2} = (a-4)^{2}
(7-a)^{2} + (2-b)^{2} = (a-4)^{2}
49 - 14a + 4 + b^{2} - 4b = 16 - 8a
b^{2} - 4b -6a + 37 = 0
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 2ndcircle.
Only difference is that it is passing through (10, -1).

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