Question
Find the locus of the point, the absolute value of the difference of the distances of which from the points (2,2) and (0,0) , is 2 . Identify the curve represented by the locus.
Answer :
Word Count : 526
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Skip in 10
Let's solve this step by step manually. We are asked: > Find the locus of the point, the absolute value of the difference of the distances of which from the points $(2,2)$ and $(0,0)$ is 2. Identify the curve. --- ### Step 1: Set up the equation Let the point be $P(x, y)$. The distance from $P$ to $(2,2)$ is: $$ d_1 = \sqrt{(x-2)^2 + (y-2)^2} $$ The distance from $P$ to $(0,0)$ is: $$ d_2 = \sqrt{x^2 + y^2} $$ The condition given is: $$ |d_1 - d_2| = 2 $$ This gives two cases: 1. $d_1 - d_2 = 2$ 2. $d_2 - d_1 = 2$ We can solve one; the other is symmetric. --- ### Step 2: Solve $d_1 - d_2 = 2$ $$ \sqrt{(x-2)^2 + (y-2)^2} - \sqrt{x^2 + y^2} = 2 $$
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