Posted by **rolan** on Friday, August 10, 2012 at 5:46am.

Point A and B of a triangle ABC are at (-1,1) and (3,9), respectively; while point C is on the parabola y=x2. Find coordinate of C so that the area of ABC is minimum, and calculate the largest are of ABC.

- math -
**Reiny**, Friday, August 10, 2012 at 8:51am
Let AB be the base, which will be a fixed length

AB = √(4^2 + 8^2) = √80

The height from C to line AB must be as long as possible, this is achieved when the slope of the tangent at C is the same as the slope of AB,

dy/dx = 2x

slope of AB = 8/4 = 2

then 2x = 2

x = 1

when x = 1, y = 1^2 = 1

C must be (1,1)

## Answer this Question

## Related Questions

- geometry - Open that link please please help me with my assignments 1. in the ...
- GEOMETRY URGENT PLEASE - (imageshack)(.)us(/)photo (/) my-images (/)42(/)2vja. ...
- geometry PLEASE - imageshack(.)(us)/photo/my-images/42/2vja.jpg/ Open that link ...
- GEOMETRY - Here are the figures. file:///C:/Users/ALIZAJOY/Pictures/Untitled....
- maths-urgently needed - In right angled triangle ABC angle B=90 degree and AB= ...
- geometry - (imageshack)123 (.)us(/)photo 123 (/) my-images 123 (/)42(/) 123 ...
- Math - A(-11,8)B(2,-6) and C(-19,-8) are the vertices of Triangle ABC. N(X,Y) is...
- Math please help - In triangle ABC, we have <BAC = 60 degrees and <ABC = ...
- Math - An equilateral triangle ABC has AB=20√3. P is a point placed in ...
- Math - An equilateral triangle ABC has AB=20√3. P is a point placed in ...