Question:
If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then
If \( (x,y) \) is equidistant from \( (a+b,b-a) \) and \( (a-b,a+b) \), then
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Square distances to avoid roots.
Updated On: May 1, 2026
- \( ax+by=0 \)
- \( ax-by=0 \)
- \( bx+ay=0 \)
- \( bx-ay=0 \)
- \( x=y \)
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The Correct Option is D
Solution and Explanation
Concept: Equidistant ⇒ distances equal.
Step 1: Write distance formula.
Step 2: Square both distances: \[ (x-a-b)^2 + (y-b+a)^2 = (x-a+b)^2 + (y-a-b)^2 \]
Step 3: Expand both sides.
Step 4: Simplify → cancel common terms.
Step 5: Final relation: \[ bx - ay = 0 \]
Step 1: Write distance formula.
Step 2: Square both distances: \[ (x-a-b)^2 + (y-b+a)^2 = (x-a+b)^2 + (y-a-b)^2 \]
Step 3: Expand both sides.
Step 4: Simplify → cancel common terms.
Step 5: Final relation: \[ bx - ay = 0 \]
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