Asked by Jodis
                The curve y=x^3-3x^2-8x+4 has tangent L at point P (-1,8). Given that the Line M is parallel to L and is also a tangent to Q show that the shortest distance between L and M is 16 root 2 
Sorry This is the correct question
            
        Sorry This is the correct question
Answers
                    Answered by
            Reiny
            
    Why not go back to your previous version and make the necessary changes ??
Once you find the x's for both P and Q, (one of the solutions has to be x = -1)
sub the other x into the equation to find point Q
You know the slope is the same for both tangents and you know that slope
so find the equation of the tangent at Q
Now use the formula for the distance between a point and a line to find your 16√2 answer
    
Once you find the x's for both P and Q, (one of the solutions has to be x = -1)
sub the other x into the equation to find point Q
You know the slope is the same for both tangents and you know that slope
so find the equation of the tangent at Q
Now use the formula for the distance between a point and a line to find your 16√2 answer
                    Answered by
            Jodis
            
    I found the x for Q to be 3 and subbing x into the equation found y-coordinate as -20
Q(3,-20)
P(-1,8)
However using the distance equation I get 20root2 not 16root2. Can you check whether my working is right?
    
Q(3,-20)
P(-1,8)
However using the distance equation I get 20root2 not 16root2. Can you check whether my working is right?
                    Answered by
            Reiny
            
    your other point is correct
so your equation of the other tangent is
y = x + b, remember the slope of both tangents is 1
plug in point (3,-20)
-20 = 3 + b
b = -23
the other tangent is y = x - 23 or x - y - 23 = 0
distance from (-1,8)
= |-1 - 8 - 23| / √(1^2 + (-1)^2 )
= 32/√2
= 32/√2 * √2/√2
= 32√2/2
= 16√2
    
so your equation of the other tangent is
y = x + b, remember the slope of both tangents is 1
plug in point (3,-20)
-20 = 3 + b
b = -23
the other tangent is y = x - 23 or x - y - 23 = 0
distance from (-1,8)
= |-1 - 8 - 23| / √(1^2 + (-1)^2 )
= 32/√2
= 32/√2 * √2/√2
= 32√2/2
= 16√2
                    Answered by
            Jodis
            
    Thanks, I calculated both tangents but was stuck on the next part. Thanks for explanation
    
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.