1.

Find the coordinates of a point on `x+y+3=0,`whose distance from `x+2y+2=0`is `sqrt(5)dot`

Answer» Let the required point be P(a,b). Then,
`a+b+3=0`
`"Also",(|a+2b+2|)/(sqrt(1^(2)+2^(2)))=sqrt5=|a+2b+2|=5`
`Rightarrow (a+2b+2=5) or (a+2b+2=-5)`
`Rightarrow a+2b=3 or a+2b=-7`
`"Thus", a+2b=3......(ii) and a+2b=-7......(iii)`
On solving (i) and (ii), we get a=-9 and b=6.
On solving (i) and (iii), we get a=1 and b=-4
Hence, the required points are A(-9,6) and B(1,-4).


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