Question

??????? \( A(3,1), B(-2,-6) \), ???? \( P \), ??????? (A)?? \( \overline{P A}=\overline{P B} \) ????? \( P \) ????????? \( \left(-\frac{5}{7}\right) \) ??? (B) ?? \( \overline{P A}+\overline{P B} \) ????????? \( P \) ????????????? (C) ?? \( \overline{P A}^{2}+\overline{P B}^{2} \) ????? \( P \) ????? (D)? \( P(t, 0) \) ?? \( |\overline{P A}-\overline{P B}| \) ????, ? \( t<0 \quad \) (E)?? \( P \) ? \( A \) ???? \( m_{1}, P \)? \( B \) ???? \( m_{2} \); ? \( m_{1} \times m_{2}=-1 \), ??? \( P \) ????????? Ans : \( A B \)

          ??????? \( A(3,1), B(-2,-6) \), ???? \( P \), ???????
(A)?? \( \overline{P A}=\overline{P B} \) ????? \( P \) ????????? \( \left(-\frac{5}{7}\right) \) ???
(B) ?? \( \overline{P A}+\overline{P B} \) ????????? \( P \) ????????????? (C) ?? \( \overline{P A}^{2}+\overline{P B}^{2} \) ????? \( P \) ????? (D)? \( P(t, 0) \) ?? \( |\overline{P A}-\overline{P B}| \) ????, ? \( t<0 \quad \) (E)?? \( P \) ? \( A \) ???? \( m_{1}, P \)? \( B \) ???? \( m_{2} \); ? \( m_{1} \times m_{2}=-1 \), ??? \( P \) ?????????
Ans : \( A B \)

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??????? A(3,1), B(-2,-6), ???? P, ???????
(A)?? P A=P B ????? P ????????? (-(5)/(7)) ???
(B) ?? P A+P B ????????? P ????????????? (C) ?? P A^2+P B^2 ????? P ????? (D)? P(t, 0) ?? |P A-P B| ????, ? t<0 (E)?? P ? A ???? m1, P? B ???? m2; ? m1× m2=-1, ??? P ?????????
Ans : A B

Added by Willie R.

Mathematical Methods in the Physical Sciences

Mary L. Boas 2nd Edition

Chapter 15

Instant Answer

Solved by Expert Marc Lauzon

Step 1

To verify this, we need to understand that the set of points equidistant from two points \(A\) and \(B\) in a plane forms the perpendicular bisector of the segment \(AB\). The slope of \(AB\) can be calculated using the coordinates of \(A(3,1)\) and \(B(-2,-6)\) Show more…

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坐標平面上兩點 \( A(3,1), B(-2,-6) \), 及一動點 \( P \), 以下哪些為真? (A)满足 \( \overline{P A}=\overline{P B} \) 之所有動點 \( P \) 所形成的圖形為斜率 \( \left(-\frac{5}{7}\right) \) 的直線 (B) 滿足 \( \overline{P A}+\overline{P B} \) 有最小值之所有動點 \( P \) 所形成的圖形不通過第二象限 (C) 滿足 \( \overline{P A}^{2}+\overline{P B}^{2} \) 有最小值的 \( P \) 在第三象限 (D)若 \( P(t, 0) \) 滿足 \( |\overline{P A}-\overline{P B}| \) 有最大值, 則 \( t<0 \quad \) (E)已知 \( P \) 與 \( A \) 的斜率為 \( m_{1}, P \)與 \( B \) 的斜率為 \( m_{2} \); 若 \( m_{1} \times m_{2}=-1 \), 則動點 \( P \) 所成的圖形為一圓形 Ans : \( A B \)

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