zaphod
Find the equation of the normal to the curve y = 3x^2-2x-1 which parellel to the line y = x-3
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zaphod
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@sauravshakya @TuringTest @satellite73
Algebraic!
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find y', set it equal to -1 and solve for x; that's an x coord. on your line.
plug into y = 3x^2-2x-1to get a y coord. you have a point and the slope now.. find the line?
myko
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1º. Find the derivative of y
2º Put it in some form you like (slope intercept, general...)
3º change it's direction vector to perpendicular
4º find x, for which it's slope is 1
zaphod
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i got the points, why is the slope 1, it has to be -1 since we take the normal line?
Algebraic!
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if slope of the tangent = -1, slope of the normal =1.
zaphod
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can u show it in a diagram?
Algebraic!
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|dw:1347988256856:dw|
zaphod
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i cant picture the problem clearly?
zaphod
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@Algebraic! where the parellel like y=x-3?
Algebraic!
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wut
zaphod
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can u show the parellel line y =x-3 in the diagram?
Algebraic!
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|dw:1347988441351:dw|
Algebraic!
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this was just a general sketch to illustrate the point. this isn't your parabola. but that's the line x-3 in black
zaphod
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why cant we directly get the gradient as m=1 instead of -1
Algebraic!
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try it and see
zaphod
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im getting a different answer and the answer is wrong
Algebraic!
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what's your answer?
zaphod
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4y =2x-5
zaphod
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dy/dx= 6x - 2
6x - 2 = 1
x= 1/2
y= -5/4
zaphod
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cn u shw the working
Algebraic!
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find y', set it equal to -1 and solve for x; that's an x coord. on your line.
plug into y = 3x^2-2x-1to get a y coord. you have a point and the slope now.. find the line?
zaphod
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why do we set it equal to -1 instead of 1?
Algebraic!
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you don't like negative one so you went with one instead? and got the wrong answer?
Algebraic!
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when the tangent to the parabola has a slope of -1, the normal at that point has a slope of 1
zaphod
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i got it thanks :)