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Find the coordinates of a point on x+y+3...

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

Text Solution

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Putting x = t in x+y+3=0, we get y=-3-t. So, let the required point be (t,-3-t). This point is at a distance of `sqrt(5)` units from x + 2y+2=0. Therefore,
`|(t-6-2t+2)/(sqrt(1^(2)+2^(2)))| = sqrt(5)`
`"or "|(-t-4)/(sqrt(5))| = sqrt(5)`
or t+4 `=+-5`
or t = 1, -9
Hence, the required points are (1,-4), and (-9,6).
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