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Question

The area (in square unit) of the triangle formed by x+y+1=0 and the pair of straight lines x2-3xy+2y2=0 is


A

712

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B

512

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C

112

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D

16

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Solution

The correct option is C

112


Explanation for correct option:

Given that a triangle is formed by x+y+1=0 and pair of straight lines x2-3xy+2y2=0

Determining the points,

Now we have,

x2-3xy+2y2=0x2-2xy-xy+2y2=0xx-2y-yx-2y=0x-yx-2y=0

Therefore, the equation of lines is,

x-y=0x=y1

And,

x-2y=0x=2y2

And, also, x+y+1=03

Using 1 in the equation 3 we get,

y+y+1=02y=-1y=-12

Put this in equation 1 we get,

x=-12

Now using 1 and 2 we get,

x=0,y=0

Now again using 2 and 3, we get,

2y+y+1=03y=-1y=-13

Therefore,

x=2yx=2-13x=-23

So, the points of the triangle are 0,0,-23,-13 and -12,-12.

Now, the area of a triangle is given by,

Area=12001-23-131-12-121=12126-16=1216=112squareunits

Therefore, the area of a triangle formed by given curves is equal to 112squareunits.

Hence, the correct answer is option (C).


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