AP EAMCET · Maths · Straight Lines
\(\mathrm{A}(4,3), \mathrm{B}(2,5)\) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoint of \(A B\), then the locus of \(P\) is
- A \(x^2+y^2-6 x-8 y=0\)
- B \(x^2+y^2-6 x-8 y \leq 0, x+y-7 < 0\)
- C \(x^2+y^2+6 x+8 y-25=0, x+y-7 \leq 0\)
- D \(x^2+y^2-6 x+8 y \geq 0, x+y-7 < 0\)
Answer & Solution
Correct Answer
(B) \(x^2+y^2-6 x-8 y \leq 0, x+y-7 < 0\)
Step-by-step Solution
Detailed explanation
Midpoint of \(AB\): \(M = \left(\frac{4+2}{2}, \frac{3+5}{2}\right) = (3,4)\) Distance condition: \((x-3)^2 + (y-4)^2 \leq 5^2 \Rightarrow x^2-6x+9+y^2-8y+16 \leq 25 \Rightarrow x^2+y^2-6x-8y \leq 0\) Equation of line \(AB\):…
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