TS EAMCET · Maths · Straight Lines
If a point \(P\) moves such that its distances from the point \(A(1,1)\) and the line \(x+y+2=0\) are equal, then the locus of \(P\) is
- A a straight line
- B a pair of straight lines
- C a parabola
- D an ellipse
Answer & Solution
Correct Answer
(C) a parabola
Step-by-step Solution
Detailed explanation
Let the co-ordinates of \(P\) are \((x, y)\) According to given condition \(\begin{aligned} & (x-1)^2+(y-1)^2=\frac{(x+y+2)^2}{2} \\ & \Rightarrow \quad 2\left(x^2+1-2 x\right)+2\left(y^2+1-2 y\right) \\ & \quad=x^2+y^2+4+2 x y+4 y+4 x \end{aligned}\)…
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