+0  
 
+1
47
4
avatar

Find the smallest distance between the origin and a point on the parabola y = x^2 - 2.

 Nov 7, 2021
 #2
avatar+18 
+2

I graphed it for you, can you take it from here now?

 

 Nov 7, 2021
 #3
avatar+115335 
+2

Thanks Bloom, the graph was a very good place to start.  Give yourself a point (I already have) laugh

 

------------

 

This question is a lot more involved than I first thought.

 

This is how I tacked it.  There is more than one way and mine might not be the easiest.

 

Let a point on the parabola by  \(K(k, k^2-2) \)     Little k is a real constant.

 

Use pytharoras's theorem to find an expression for the square of the distance between  the origin and K.  Call it D

 

Now use calculus to find the minimum D

 

etc

Draw a pic to help you.

 

I will help more if you work with me towards the solution.   

ie    show what you can do so far and discuss your problems with me.

 Nov 7, 2021
edited by Melody  Nov 7, 2021
edited by Melody  Nov 7, 2021
 #4
avatar+18 
+2

Hi Melody! Thanks for the compliment! :D Also thanks for the point! :D

Bloom  Nov 10, 2021

23 Online Users

avatar
avatar
avatar