Circle 3 Question 1

1. The common tangent to the circles x2+y2=4 and x2+y2+6x+8y24=0 also passes through the point

(2019 Main, 9 April II)

(a) (6,2)

(b) (4,2)

(c) (6,4)

(d) (4,6)

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Answer:

Correct Answer: 1. (a)

Solution:

  1. Given circles are x2+y2=4, centre c1(0,0) and radius r1=2

and x2+y2+6x+8y24=0, centre c2(3,4) and radius r2=7

c1c2=9+16=5 and |r1r2|=5

c1c2=|r1r2|=5

circle x2+y2=4 touches the circle x2+y2+6x+8y24=0 internally.

So, equation of common tangent is

S1S2=0

6x+8y20=0

3x+4y=10

The common tangent passes through the point (6,2), from the given options.



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