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Question

Find the equation of the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x2+2xy+3y2+4x+8y11=0


A

7x22xy+y2=0

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B

7x22xyy2=0

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C

7x2+2xy+y2=0

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D

7x2+2xy+y2=0

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Solution

The correct option is B

7x22xyy2=0


We will use method of homogenization to solve this. The combination of pairs straight lines is given by
Ax2+2hxy+by2+2gx(lx+myn)+2fy(lx+myn)+c(lx+myn)2=0

the term equivalent to lx+myn is y3x2. We can take (3xy2) also.
x2+2xy+3y2+4x(y3x2)+8x(y3x2)-11x(y3x2)2
x2+2xy+3y2+2xy6x2+4y212xy114(y2+9x26xy)=0
5x2+7y28xy11y299x2+66xy4=0
20x2+28y232xy11y299x2+66xy=0
119x2+17y2+34xy=0
7x22xyy2=0


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