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Question

If point $$P(h,k)$$ lies on the line $$2x + 3y = 5$$ such that $$|PA .PB|$$ is maximum where $$A(2,3)$$ and $$B(1,2)$$ then the value of $$(3h + 2k)$$ is


A
3
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B
2
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C
6
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D
4
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Solution

The correct option is C $$4$$
$$| PA - PB| < AB$$
$$|PA PB|_{max} = AB$$
In this case P, A & B are collinear
So 'P' is intersecting point of these two lines as shown in figure
Equation of AB: $$\left.\begin{matrix}
y-x & =1\\ 
2x+3y & =5
\end{matrix}\right\}$$
$$\Rightarrow$$ Intersection point $$P\left (\dfrac {2}{5}, \dfrac {7}{5}\right )$$
$$\therefore 3h+2k=4$$
344557_290734_ans_adc5dc35b949442cbb23e4e139b6198b.png

Mathematics

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