The radius of the circle touching the line x + y = 4 at 1,3 and intersecting x 2 + y 2 = 4 orthogonally is

Question

The radius of the circle touching the line x + y = 4 at 1,3 and intersecting x 2 + y 2 = 4 orthogonally is, 3 2 4 units, 3 4 units, 3 2 units, 4 2 3 units

MARKS App · Accepted Answer

Let the equation of the circle is x - 1 2 + y - 3 2 + λ x + y - 4 = 0 ⇒ x 2 + y 2 + λ - 2 x + λ - 6 y + 10 - 4 λ = 0 which is orthogonal to x 2 + y 2 = 4 Now, 2 g 1 g 2 + 2 f 1 f 2 = c 1 + c 2 implies 0 + 0 = 10 - 4 λ - 4 ⇒ λ = 3 2 Hence, the equation of the circle is x 2 + y 2 - x 2 - 9 y 2 + 4 = 0 R a d i u s = 1 16 + 81 16 - 4 = 18 16 = 3 2 4

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