AP EAMCET · Maths · Straight Lines
If \(P\) is a variable point such that the sum of the distances from \(P\) to the points \(A(2,2)\) and \(B(2,-2)\) is 4, then the locus of \(P\) represents
- A an ellipse
- B a vertical line
- C segment of a vertical line
- D segment of a horizontal line
Answer & Solution
Correct Answer
(C) segment of a vertical line
Step-by-step Solution
Detailed explanation
The sum of the distances from \(P(x,y)\) to points \(A(2,2)\) and \(B(2,-2)\) is \(PA + PB = 4\). The distance between points \(A\) and \(B\) is \(AB = \sqrt{(2-2)^2 + (2-(-2))^2} = \sqrt{0^2 + 4^2} = 4\). Since \(PA + PB = AB\), the locus of point \(P\) is the line segment…
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