TS EAMCET · Maths · Straight Lines
Let \(A(2,1)\) be a point and equation of the straight line \(L\) be \(x-y=0\). Let \(a\) and \(b\) respectively represent the distances from a variable point \(P(\alpha, \beta)\) to \(A\) and to the line \(L\). If \(C\) is distance of the point \(A\) from origin such that \(a=b c\), then locus of \(P\) is
- A \(3 x^2+3 y^2+10 x y+8 x+4 y+10=0\)
- B \(3 x^2+3 y^2-10 x y+8 x+4 y-10=0\)
- C \(3 x^2+2 y^2-10 x y+8 x+4 y+10=0\)
- D \(2 x^2+3 y^2-10 x y-8 x-4 y-10=0\)
Answer & Solution
Correct Answer
(B) \(3 x^2+3 y^2-10 x y+8 x+4 y-10=0\)
Step-by-step Solution
Detailed explanation
Given equation of line \(x-y=0\) Distance from \(P(\alpha, \beta)\) to line \(x-y=0\) is \(b=\left|\frac{\alpha-\beta}{\sqrt{2}}\right| \Rightarrow(\alpha-\beta)^2=2 b^2\) \(\ldots(i)\) Distance between \(P(\alpha, \beta)\) and \(A(2,1)\) is \(a^2=(\alpha-2)^2+(\beta-1)^2\)…
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