Question

Find the equation of the locus of a point which forms a triangle of area 7 and points A(4,5) B(-2,3)

Answer 1

Answer:

Let P(x

1

,y

1

) be point on the locus, (x

2

,y

2

)=(2,3) and (x

3

,y

3

)=(−1,4)

Given, area of △PAB = 5 sq. units

Therefore,

2

1

∣

∣

∣

∣

∣

∣

x

1

−2

y

1

−3

2−(−1)

3−4

∣

∣

∣

∣

∣

∣

=5

∣

∣

∣

∣

∣

∣

x

1

−2

y

1

−3

3

−1

∣

∣

∣

∣

∣

∣

=10

−(x

1

−2)−3(y

1

−3)=±10

x

1

+3y

1

+11=±10

Required equation is x+3y=10−11 or x+3y=−10−11

That is,

x+3y+1=0 or x+3y+21=0.

Step-by-step explanation:

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