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The equation of tangent to the curve y=x...

The equation of tangent to the curve `y=x^(2)+4x+1` at (-1, -2) is

A

`2x-y=0`

B

`2x+y-5=0`

C

`2x-y-1=0`

D

`x+y-1=0`

Text Solution

Verified by Experts

The given equation of the curve is,
`y=x^(2)+4x+1.`
On differentiating w.r.t.x, we get
`(dy)/(dx)=2x+4`
`therefore ((dy)/(dx))_(x=-1)=2(-1)+4=-2+4=2.`
The equation of the tangent at `(-1,2)` is,
`y-(-2)=2(x-(1))`
`y+2=2(x+1)`
` y+2=2x+2`
`2x-y=0`
Hence, the correct answer from the given alternative is (a).
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