TS EAMCET · Maths · Straight Lines
Let \(Q\left(x_1, y_1\right)\) be a variable point and \(R(1,0)\) be a point on the circle \(x^2+y^2=1\) and \(P\) be the mid-point of \(Q R\). Then, the locus of the point \(P\) is
- A \(x^2+y^2-2 x=0\)
- B \(x^2+y^2+x=0\)
- C \(x^2+y^2+2 x=0\)
- D \(x^2+y^2-x=0\)
Answer & Solution
Correct Answer
(D) \(x^2+y^2-x=0\)
Step-by-step Solution
Detailed explanation
Let point \(P(h, k)\). \(P\) is mid-point of \(Q R\). \[ \therefore h=\frac{x_1+1}{2}, k=\frac{y_1}{2} \Rightarrow x_1=2 h-1, y_1=2 k \text {. } \] \(\left(x_1, y_1\right)\) lie, on the circle \(x^2+y^2=1\) \[ \therefore(2 h-1)^2+(2 k)^2=1 \Rightarrow h^2+k^2-h=0 \]…
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