JAMB - Mathematics (2001 - No. 22)
Find the locus of a point which moves such that its distance from the line y = 4 is a constant, k.
y = 4 \(\pm\) k
y = k \(\pm\) 4
y = 4 + k
y = k - 4
Explanation
The line y = 4 is a horizontal line in the Cartesian plane. The distance from any point( x, y) to this line is given by d = | y - 4| and this distance to be equal to k
| y - 4 | = k
case1, y - 4 = k, y = k + 4 ⇒ 4 + k
case2, y - 4 = - k, y = - k + 4 ⇒ 4 - k
combining the two solutions above, we have y = 4 \(\pm\) k
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