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Q.

Let circle C be the image of x2 + y2 – 2x + 4y – 4 = 0 in the line 2x – 3y + 5 = 0 and A be the point on C such that OA is parallel to x-axis and A lies on the right hand side of the centre O of C. If B(α,ß), with ß < 4, lies on C such that the length of the arc 
AB is (1/6)th of the perimeter of C, then β3α is equal to

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a

3+3

b

4-3

c

3

d

4

answer is D.

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Detailed Solution

Question Image

Centre (1, –2), r = 3 
Reflection of (1, –2) about 2x – 3y + 5 = 0
x12=y+23=2(2+6+5)13=2x=3,y=4
 Equation of circle ‘C’ 
C : (x+3)2 + (y– 4)2 = 9 
 A.T.Q.
Question Image
(arcAB)=16×2πr=16×2πrθ=π3(α+6)2+(β4)2=27(α+3)2±(β4)2=9(α+6)2(α+3)2=186α=9α=32,β=4332β3α4332+332=4

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Let circle C be the image of x2 + y2 – 2x + 4y – 4 = 0 in the line 2x – 3y + 5 = 0 and A be the point on C such that OA is parallel to x-axis and A lies on the right hand side of the centre O of C. If B(α,ß), with ß < 4, lies on C such that the length of the arc AB is (1/6)th of the perimeter of C, then β−3α is equal to