Question

A(2,3),B(-3,4) are two points.if a point P moves such that the area of triangle ∆PAN is 8.5 squarr units, then find the locus of P.

Answer 1

$\textbf{Given:}$

$A(2,3)\;\text{and}\;B(-3,4)\;\text{and P is the moving point}$

$\textbf{To find:}$

$\text{Locus of P}$

$\textbf{Solution:}$

$\text{Let the moving point P be (h,k)}$

$\text{Since area of \triangle PAB is 8.5 square units, we have}$

$\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]=8.5$

$\dfrac{1}{2}[h(3-4)+2(4-k)-3(k-4)]=8.5$

$h(-1)+2(4-k)-3(k-3)=17$

$-h+8-2k-3k+9=17$

$-h-5k=0$

$h+5k=0$

$\textbf{Answer:}$

$\textbf{The locus of P is \bf\,x+5y=0 }$

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