The normal line to a curve C at a point P is, by definition, the line that passes through P and is perpendicular to the tangent line to C at P. Find the equation of the normal line to the parabola y=−3−x^2 at the point (2,−7) .

Question

The normal line to a curve C  at a point P  is, by definition, the line that passes through P and is perpendicular to the tangent line to C at P. Find the equation of the normal line to the parabola y=−3−x^2 at the point (2,−7) .

anonymous · Answer

can you find what is the slope of the parabola at the given point?

anonymous · Answer

I don't know. I don't know how to even approach this problem!

anonymous · Answer

what does the slope of a line represent in general terms?

anonymous · Answer

its the rate of change, do you know any other function that represents rate or change?

anonymous · Answer

no

anonymous · Answer

derivatives mean rate of change

anonymous · Answer

does that mean I need to find the derivative of the given function?

anonymous · Answer

yes

anonymous · Answer

and that's -2x

anonymous · Answer

so thats the slope of the parabola, can you find the equation of the tangent at the point?

anonymous · Answer

is this where I use y-y=m(x-x)

anonymous · Answer

yeah, that is the point slope formula.

anonymous · Answer

is this right? y-(-7)=-2x(x-2)

anonymous · Answer

no, the slope in general is -2x, but you need the slope at a certain point.

anonymous · Answer

Can you just tell me step by step on how to do this?

anonymous · Answer

so the slope at any point on the par is -2x but you know what x you are interested in right? x=2 so the slope there is -4

anonymous · Answer

so now do I just plug the -4 into the slope formula?

anonymous · Answer

follow?

anonymous · Answer

y-(-7)=-4(x-2)?

anonymous · Answer

I don't understand

anonymous · Answer

sorry, i'm not getting notifications. The slope of the tangent at that point is -4, you wan the equation of the normal line. like the question says the normal line is perpendicular. that means it has an inverse slope. do you know what the inverse of -4 is?

anonymous · Answer

the answer to this question is due at 12 tonight. Can you just give me the answer and the after we can talk about why its the answer?

anonymous · Answer

its only a few steps

anonymous · Answer

then tell me the steps pleaseeeeeeeeeee

anonymous · Answer

you need the inverse of the slope to get the perpendicular slope and you already know the point so you can use the point slope formula

anonymous · Answer

whats the inverse of the slope?

anonymous · Answer

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does that help?