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
- A \(x^2-2 x y+y^2-2 x-2 y+4=0\)
- B \(x^2+2 x y+y^2-2 x-2 y+4=0\)
- C \(x^2-2 x y+y^2+2 x+2 y+4=0\)
- D \(x^2-2 x y-y^2+2 x+2 y+4=0\)
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…
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