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0 votes
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in Mathematics by (75.1k points)

The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 – 6x – 8y – 24 = 0 is …….

(a) 0

(b) 1

(c) 2

(d) None of these

1 Answer

+1 vote
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Best answer

The correct option (b) 1

Explanation:

 x2 + y2 = 4 ⇒ c1 = centre (0, 0) and r1 = 2

x2 + y2 – 6x – 8y – 24 = 0 ⇒ c2 = (3, 4) and r2 = √(32 + 42 + 24) = 7

Now    r2 – r1 = 7 – 2 = 5

and     c1c2 = √(32 + 42) = 5

∴    c1c2 = r2 – r1

∴ Given circle touches internally such that they have one common tangent at point of contact.

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