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The equation of the line(s) parallel to ...

The equation of the line(s) parallel to `x-2y=1` which touch(es) the circle `x^2+y^2-4x-2y-15=0` is (are) `x-2y+2=0` (b) `x-2y-10=0` `x-2y-5=0` (d) 3`x-y-10=0`

A

`x-2y+2=0`

B

`x-2y-10=0`

C

`x-2y-5=0`

D

`x-2y+10=0`

Text Solution

Verified by Experts

The correct Answer is:
2,4
Let the equation of the tangent be
`x-2y = k` (i)
Line `(i)` touches the circles. Therefore,
Distance from center to line `(i) =` Radius of circle
or `(|2-2-k|)/(sqrt(5))=sqrt(4+1+15)`
or `|k| = 10` or `k = +-10` .
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