annabethxchase
Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

help with 5 please( question tuped below too).

Prove that y=x+2 is a tangent to the locous P(2t²,4t).

find the point of contact of this tangent to this locous and hence find the equation of normal at the point.


thanks
​

Help With 5 Please Question Tuped Below Too Prove That Yx2 Is A Tangent To The Locous P2t4tfind The Point Of Contact Of This Tangent To This Locous And Hence Fi class=

Sagot :

sqdancefan

9514 1404 393

Answer:

  • tangent point: (2, 4)
  • normal: y = -x +6

Step-by-step explanation:

The derivative of P with respect to t is ...

  P' = (x', y') = (4t, 4)

so the slope of the curve for some value of t is ...

  dy/dx = y'/x' = 4/(4t) = 1/t

The line we want to be a tangent is y = x +2, which has a slope of 1. The curve will have a slope of 1 where ...

  1/t = 1   ⇒   t = 1

At t=1, the point P is (2·1², 4·1) = (2, 4). For x=2, the point on the desired tangent is y = x +2 = 2 +2 = 4, or (x, y) = (2, 4).

The curve and the given line both have a slope of 1 at the point (2, 4), so that is the tangent point.

__

The normal to the curve at (2, 4) will have a slope that is the opposite reciprocal of the slope of the tangent: -1/1 = -1. Then point-slope form of the equation of the normal line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -4 = -1(x -2) . . . . . . line with slope -1 through point (2, 4)

  y = -x +6 . . . . . . . . equation of the normal line in slope-intercept form

View image sqdancefan
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.