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A circle rolls between pair of lines 9x^...

A circle rolls between pair of lines `9x^(2)+24xy +16y^(2) - 25 =0` touching both of them. Then its area is

A

`4pi` sq. units

B

`8pi` sq. units

C

`12pi` sq. units

D

`pi` sq. units

Text Solution

Verified by Experts

The correct Answer is:
D
We have `9x^(2) +24 xy +16y^(2) - 25 = 0`
`rArr (3x +4y)^(2) - 25 =0`
`rArr 3x +4y +5 =0` or `3x +4y -5 =0`
These lines are parallel and tangents to the circle
`:'` Distance d between parallel tangents = diameter of the circle
`:. d = (|5-(-5)|)/(sqrt(3^(2)+4^(2))) =2`
`:.` Radius `= r =1`
`:.` Area of circle `= pi` sq. units
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