Results 1 to 2 of 2

Math Help - Find area of triangle bounded by a normal and a tangent to a curve.

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Find area of triangle bounded by a normal and a tangent to a curve.

    The tangent and normal to the curve y=4\sqrt{x+2} at the point P(7,12) cut the x-axis at points M and N respectively. Calculate the area of the triangle PMN.

    My attempt is...

    \frac{dy}{dx}=\frac{2}{\sqrt{x+2}}

    Tangent : y-12=\frac{2(x-7)}{\sqrt{x+2}}

    I guess I need some help in solving for x...
    Last edited by mr fantastic; February 18th 2010 at 02:03 AM. Reason: Changed post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Feb 2010
    Posts
    66
    Quote Originally Posted by Punch View Post
    The tangent and normal to the curve y=4\sqrt{x+2} at the point P(7,12) cut the x-axis at points M and N respectively. Calculate the area of the triangle PMN.

    My attempt is...

    \frac{dy}{dx}=\frac{2}{\sqrt{x+2}}

    Tangent : y-12=\frac{2(x-7)}{\sqrt{x+2}}

    I guess I need some help in solving for x...
    From your dy/dx you can find the slope of the tangent at x = 7. You will also then have the slope of the normal as its negative inverse. YOu should find those as 2/3 and -3/2.

    You can then have the equation of the tangent as (y-12)/(x - 7) = 3/2.
    Let x = 0 to find the y intercept.

    Do the same for the normal.

    You should now be able to find the lengths of the line segments PM and PM, which are perpendicular to each other, so easily calculating the area of the triangle.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find curve that has tangent and normal lines that create a triangle
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 12th 2011, 08:13 AM
  2. Area bounded by curve and tangent line
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 10th 2010, 05:19 PM
  3. Replies: 3
    Last Post: December 29th 2009, 04:02 PM
  4. Replies: 1
    Last Post: November 12th 2009, 01:35 PM
  5. Find area bounded by the curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 5th 2009, 09:15 PM

Search Tags


/mathhelpforum @mathhelpforum