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Question

If A is (x1,y1) where x1=1 on the curve y=x2+x+10, the tangent at A cuts the x-axis at B. The value of ¯¯¯¯¯¯¯¯OA.¯¯¯¯¯¯¯¯AB is

A
148
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B
352
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C
140
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D
148
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Solution

The correct option is C 148
when x1=1,y1=1+1+10=12
dydx=2x+1 At (x1,y1),dydx= slope of tangent =3
Tangent passes through (1,12) and has slope = 3
its equation : y12=3(x1)
y=3x+9
At x-axis,y=0x=3BI(3,0)
¯¯¯¯¯¯¯¯OA=^i+12^j ¯¯¯¯¯¯¯¯AB=4^i12^j
OA.AB=4144=148(A)


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