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The line joining the points A(2,1) and B...

The line joining the points `A(2,1)` and `B(3,2)` is perpendicular to the line `(a^2)x+(a+2)y+2=0.` Find the values of `a`.

Text Solution

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The correct Answer is:
`a=2,-1`
The slope of the line joining `A(2,1) and B(3,2)` is `(2-1)/(3-2)=1`
The slope of the line `(a^2)x+2)y+2=0` is `(a^2)/(a+2)`
The lines are perpendicular. Therefore, `((a^2)/(a+2))(1)=-1`
or `a^2=a+2`
or `a^2-a-2=0`
or `(a-2)(a+1)=0`
or `a=2,-1`
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