Question
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
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
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?
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
Jodis
Thanks, I calculated both tangents but was stuck on the next part. Thanks for explanation