1.

Equation of a circle passing through (2, 8) and touching the lines 4x-3y-24=0 and4x+3y-42=0 having x-coordinates of the centre less than or equal to 8 is

Answer»

`(x-2)^(2)+(y+3)^(2)=25`
`(x-2)^(2)+(y-3)^(2)=16`
`(x-2)^(2)+(y-3)^(2)=25`
`(x+2)^(2)+(y-3)^(2)=25`

Solution :Let centre of circle be C(a,b)
Circle TOUCH both LINES
`r= |(4a-3b-24)/(5)|=|(4a+3b-42)/(5)|= sqrt((a-2)^(2) + (b-8)^(2))`
Solve these PAIR WISE b=3 and a=2, r=5
Equation of circle `(x-2)^(2) + (y-3)^(2)=25`.


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