Thread: minimum value help

Hello,
I am stuck with this question ,:

find the minimum value of where are real numbers with justify your answer

can someone help please?

is the distance squared from the point (-1,0) to (x,y)
So the question is asking the square of the minimum distance from (-1,0) to any point on the line .
i.e. the square of the distance from the point (-1, 0) to the line
you should get the distance to be ,
and minimum

Hi thanks for your reply...
I don't understand where the (-1,0) points appeared from....

But I done it this way, could someone tell me if this way is correct please?

= 2

What is the formula for the distance from (x,y) to (-1,0)?
sqrt((x+1)^2 + y^2) right? So the square of the distance is your formula.

You made a mistake in your steps:
(1 + x)^2 = 1 + 2x + x^2
(1 - x)^2 = 1 - 2x + x^2

could you show me how you got the distance to be the sqrt2 please

Actually, your approach is easier.



Now clearly is minimum when , which gives 2.

If you want to know the distance to line approach (don't worry about it, if you haven't learned this):
Rearranging, the line equation is
The slope of the perpendicular line has m = 1
A perpendicular line with m = 1 through point (-1, 0) has the equation
Intersection of the line and the perpendicular line is at (0,1)
So the minimum distance is from (-1,0) to (0,1) which is sqrt(2).

If you are confused on some step, draw a diagram and the graphs.

Thanks

Originally Posted by wolfhound

Hello,
I am stuck with this question ,:

find the minimum value of where are real numbers with justify your answer

can someone help please?

minimum when x=0.