AP EAMCET · Maths · Straight Lines
If the origin is shifted to a point P by the translation of axes to remove the \(y\)-term from the equation \(x^2-y^2+2 y-1\) \(=0\). then the transformed equation of it is
- A \(x^2-y^2=1\)
- B \(x^2-y^2=0\)
- C \(x^2+y^2=1\)
- D \(x^2+y^2=0\)
Answer & Solution
Correct Answer
(B) \(x^2-y^2=0\)
Step-by-step Solution
Detailed explanation
\(x^2+y^2+2 y-1=0\) let \(x=X, y=Y+h \Rightarrow X^2-(Y+h)^2+2(Y+h)-1=0\) \(\Rightarrow X^2-Y^2+2(1-h) Y-h^2+2 h-1=0\) To remove \(y\)-term, \(h=1\) \(\Rightarrow X^2-Y^2=0\) is the transformed equation
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