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Question

If the lines joining the origin to the intersection of the line y=mx+2 and the circle x2+y2=1 are at right angles, then:


A

m=3

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B

m=±7

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C

m=1

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D

m=5

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Solution

The correct option is B

m=±7


Explanation for the correct option

Given the lines joining the origin to the intersection of the line y=mx+2 and the circle x2+y2=1 are at right angles.

The equation of the lines joining origin and point of intersection of the line given and the circle will be

x2+y2=y-mx22

4x2+y2=y2+m2x2-2mxy

x2(4-m2)+y2(4-1)+2mxy=0

x2(4-m2)+2mxy+3y2=0

Now since these lines are at right angles, so, coefficientofx2coefficientofy2=-1

4-m23=-14-m2=-34-m2+3=0m2=7m=±7

Hence, option (B) i.e. m=±7 is the correct answer.


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