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Two circles are drawn through the points (a,5a) and (4a,a) to touch the axis of y. Find the angle at which they intersect.

Two circles are drawn through the points (a,5a) and (4a,a) to touch the axis of y. Find the angle at which they intersect.

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
letx^2 + y^2 + 2gx + 2fy + c = 0 be the eqn of circle which has 3 variables g,f, and c.

now if passes thruthe points (a,5a) and (4a,a) so they will satisfy in the eqn

hence we get 2 eqns

also it touches y axis hence f^2 – c = 0 ------(3)

Now solve eqn 1, 2 and 3 and find the circles and hence find angle between them

Thanks

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