Hyperbola exercise - Hard 4 me

[Anonymm]

Hi, I can't handle one example of a hyperbola: Verify that the point T [-2; 2] lies on the hyperbola h: 4x^2-y^2-12 = 0. Next, write the equation of the tangent of the hyperbola at this tangent point.
Could someone please explain the procedure to me?
Thanks so much for the answers.

 

[firemath]

Hello there!
What have you tried so far? Where are you stuck? What class are you taking? We can give better help if you reveal these things!


Here's the graph for you to work with:


You can see that point T does lie on the graph of the hyperbola.

 

[Steven G]

You are given the x-value and y-value of a point. You want to know if it is on the hyperbola you are given the equation of. This equation is the set of ALL points which are on the hyperbola. You just need to verify that this given point is on the hyperbola. Do you know how to do that?

How to write the equation of the tangent line you can not do, as far as I can see, with only Geometry and Trigonometry (which is where you posted your question). Have you studied Calculus? Were you given the slope formula for any given point on the hyperbola?

For now please try to do the first part.

 

[Anonymm]

Oh, sorry.

Hello there!
What have you tried so far? Where are you stuck? What class are you taking? We can give better help if you reveal these things!


Here's the graph for you to work with:
View attachment 18408

You can see that point T does lie on the graph of the hyperbola.

Oh, sorry for that. I've tried this (in attached file). I go into third year at the high school.

 

[Anonymm]

You are given the x-value and y-value of a point. You want to know if it is on the hyperbola you are given the equation of. This equation is the set of ALL points which are on the hyperbola. You just need to verify that this given point is on the hyperbola. Do you know how to do that?

How to write the equation of the tangent line you can not do, as far as I can see, with only Geometry and Trigonometry (which is where you posted your question). Have you studied Calculus? Were you given the slope formula for any given point on the hyperbola?

For now please try to do the first part.

I did it this way (in attached file). I come from the Czech Republic, so I don't know your sections. We call this analytic geometry.

 

[Steven G]

OK, very good. You verified that the point (-2,2) is on the hyperbola.

1st part of Calculus is the study of derivatives. Have you learned about derivatives?

Does dy/dx = 4x/y makes sense to you?

Do you have an example of how to do a similar problem for finding the equation of the tangent line?

 

[Anonymm]

We haven't discussed the derivation yet, so it's a big unknown to me...

 

[Steven G]

We haven't discussed the derivation yet, so it's a big unknown to me...

Do you have an example from notes or from your textbook showing how to do such problems. You have a point on the line you want to find, namely (-2,2). Now you need the slope of this tangent line. I need help in knowing what method you have been taught on how to find this slope. If you don't answer this question it is very hard to help you.

 

[Anonymm]

 

[Steven G]

View attachment 18418

This is called derivates. If you have y =x^2 then dy/dx = 2x NOT 1 =2x. The derivative of a y term must have a factor of dy/dx or y'

The derivative of x^2 is 2x NOT i2x. The derivative of -y^2 is -2y dy/dx or -2yy'
The derivative of 1 is NOT 1. What is it?

Please try again. You are close.