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Minhoe
Minhoe asked in Science & MathematicsMathematics · 7 years ago

How do I convert this equation into ax+by+c= 0 form?

So the question I got was :

'A curve has equation y = x^3+ 2x^2-9x +3

Work out the equation of the normal to this curve at the point (1, -3)'

I got an equation for the normal as being, y= 1/2x -1, but how can I give this in ax + by +c = 0 form. The answer is x-2y-7=0 but how do you get this??

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  • hayharbr
    Lv 7
    7 years ago

    You couldn't; it would get multiplied by 2 and go to 2y = x - 2 then x - 2y - 2 = 0

    You know the tangent's slope is 3x^2 + 4x - 9 which if x = 1 is -2

    That means the normal's slope is the opposite reciprocal which you correctly said is 1/2

    Point slope form: y + 3 = 1/2 (x - 1)

    y + 3 = 1/2 x - 1/2

    Multiply by 2

    2y + 6 = x - 1

    so 0 = x - 2y - 7

  • Kyle
    7 years ago

    first, multiply by 2 to get 2y=x-2

    then subtract 2y from both side to get x-2y-1=0

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