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AP EAMCET · Maths · Straight Lines

If the equations \(\mathrm{x}=\mathrm{t}^2+\mathrm{t}+1, \mathrm{y}=\mathrm{t}^2-\mathrm{t}+1\) represents a curve \(\mathrm{C}\) with parameter \(\mathrm{t}\), then the Cartesian equation of \(\mathrm{C}\) is

  1. A \(x^2-2 x y+y^2-2 x-2 y+4=0\)
  2. B \(x^2+2 x y+y^2-2 x-2 y+4=0\)
  3. C \(x^2-2 x y+y^2+2 x+2 y+4=0\)
  4. D \(x^2-2 x y-y^2+2 x+2 y+4=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^2-2 x y+y^2-2 x-2 y+4=0\)

Step-by-step Solution

Detailed explanation

Given \(\mathrm{x}=\mathrm{t}^2+\mathrm{t}+1, \mathrm{y}=\mathrm{t}^2-\mathrm{t}+1\) Now, \(x+y=2\left(t^2+1\right)\) ... (i) \(\mathrm{x}-\mathrm{y}=2 \mathrm{t}\)... (ii) From (i) \& (ii), we get…