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Math Help - Tangent passes through a particular point.

  1. #1
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    Tangent passes through a particular point.

    Hello,

    I am new to this forum and am having difficulty with a particular question (I have searched for the answer, but have come up with nothing). Help is greatly appreciated

    Question:

     y= -3x^2 - 6.14 Determine the positions on the curve (x,y), of all tangents that pass through the point (2.53,25.34).

    I really don't understand the question at all, so any help in working would be great.

    Thanks in advance
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  2. #2
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    Quote Originally Posted by missb View Post
    Hello,

    I am new to this forum and am having difficulty with a particular question (I have searched for the answer, but have come up with nothing). Help is greatly appreciated

    Question:

     y= -3x^2 - 6.14 Determine the positions on the curve (x,y), of all tangents that pass through the point (2.53,25.34).

    I really don't understand the question at all, so any help in working would be great.

    Thanks in advance
    Drawing a picture will help ....

    At the point (a, b):

    b = -3a^2 - 6.14 .... (1)

    m = \frac{dy}{dx} = -6a .... (2)

    m = \frac{b - 25.34}{a - 2.53} .... (3)

    Solve these three equations simultaneously for a and b.
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  3. #3
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    Thank you for the quick reply!

    From my understanding, m is the first derivative of the original equation, m is usually how you calculate the slope in the form of m=\frac{y2-y1}{x2-x1} right?

    In your response, b is the original equation, so what is a? And do you use the quadratic formula to calculate a and b?

    Sorry if this seems an obvious question, but I really just don't get it
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  4. #4
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    Quote Originally Posted by missb View Post
    Thank you for the quick reply!

    From my understanding, m is the first derivative of the original equation, Mr F says: Correct.

    m is usually how you calculate the slope in the form of [tex]m=\frac{y2-y1}{x2-x1}[\math] right? Mr F says: Correct. That's where equation (3) comes from.

    In your response, b is the original equation, so what is a? Mr F says: (a, b) is the point on the curve that you're trying to find.

    And do you use the quadratic formula to calculate a and b? Mr F says: If I was you, I'd substitute (1) into (3) and then equate (2) and (3). Now solve the resulting equation for a. etc.

    Sorry if this seems an obvious question, but I really just don't get it
    Draw a picture.
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