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Question

The equation of pair of lines joining the origin to the point of intersection of x2+y2=9 and x+y=3 is:


A

(x2+-x)2=9

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B

xy=0

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C

(3+y)2+y2=9

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D

(x-y)2=9

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Solution

The correct option is B

xy=0


Finding the point of intersection of x2+y2=9 and x+y=3:

x+y=3y=3-xx2+(3-x)2=9Substitutingyinx2+y2=92x2-6x+9=92x2-6x=0x2-3x=0x(x-3)=0x=0or3y=3or0

Therefore, the point of intersection are (0,3)and(3,0).

We have to find the equation of the pair of lines that joins the origin to the points (0,3)and(3,0).

We know that, (0,3) lies on the y-axis while (3,0) lies on the x-axis. Hence, the equation of (0,3) is x=0and the equation of the point (3,0) is y=0.

Therefore, the equation of the pair of lines is: xy=0.

Hence, the correct answer is Option (B).


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