Find The Radius Of Smaller Circle Which Touches The Straight Line 3x – y = 6 At (1, –3) And Also Touches The Line y = x.

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Question

Find the radius of smaller circle which touches the straight line 3x – y = 6 at (1, –3) and also touches the line y = x.

diffcult

Solution

Correct option is

1.5

Let C (h, k) be the centre of the circle. Let AB and C’D be the lines represented by 3x – y = 6 and y = x respectively.

Clearly, the circle touches AB at A (1, –3).

Equation of line ⊥ to 3x – y = 6 is x + 3y = λ which passes through (1, –3).

Then 1 – 9 = λ

Which passes through C (h, k)

then h + 3k + 8 = 0 …(1)

Now centre

Since radius from (2),

Hence radius of smaller circle is 1.5 units.

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