Question

Find the point on the line −6x+4y−1=0 which is closest to the point (1−4). My assignment is due in half an hour please help asap. :(

Answer 1

Closest to the point (1, -4). *

Answer 2

ok do you need work or answer or both?

Answer 3

Just the answer would be good. Thanks a lottt

Answer 4

here is the idea. first solve for y get
\[y=\frac{3}{2}x+\frac{1}{4}\] then any point on the line will look like
\[(x,\frac{3}{2}x+\frac{1}{4})\] and the square of the distance between that point and (1,-4) will be
\[(x-1)^2+(\frac{3}{2}x+\frac{1}{4}+4)^2\] then algebra to simplify.

Answer 5

here is the algebra
http://www.wolframalpha.com/input/?i=%28x-1%29%5E2%2B%283x%2F2%2B1%2F4%2B4%29%5E2

Answer 6

Ok but then what do I do with it?

Answer 7

you can see also the derivative is
\[\frac{1}{4}(26x+43)\] set this equal to zero and solve for x. that will give the x - coordinate of the minimum which wolfram also solves for you as
\[x=-\frac{43}{26}\]

Answer 8

notice that wolfram not only simplified but gave the derivative and also the minimum value. that is your x, substitute to find the y and you are done.
in under half an hour

Answer 9

Got it. Thankssss a lot!

Answer 10

Can you by any chance help me with this problem as well? I would really appreciate it!!!
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=1−x2. What are the dimensions of such a rectangle with the greatest possible area?

Answer 11

y=1-x^2 *

Answer 12

Hey are you there? Please it's really important.