Circle 4 Question 6

6. The circle passing through the point (1,0) and touching the Y-axis at (0,2) also passes through the point

(2011)

(a) 32,0

(b) 52,2

(c) 32,52

(d) (4,0)

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Answer:

Correct Answer: 6. (d)

Solution:

  1. Equation of circle passing through a point (x1,y1) and touching the straight line L, is given by

(xx1)2+(yy1)2+λL=0

Equation of circle passing through (0,2) and touching x=0

(x0)2+(y2)2+λx=0

Also, it passes through (1,0)1+4λ=0

λ=5

Eq. (i) becomes,

x2+y24y+4+5x=0x2+y2+5x4y+4=0

For x-intercept put y=0x2+5x+4=0,

(x+1)(x+4)=0x=1,4

Hence, (d) option (4,0).



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