Thread: Tangent passes through a particular point.

Hello,

I am new to this forum and am having difficulty with a particular question (I have searched for the answer, but have come up with nothing). Help is greatly appreciated

Question:

Determine the positions on the curve (x,y), of all tangents that pass through the point (2.53,25.34).

I really don't understand the question at all, so any help in working would be great.

Thanks in advance

Originally Posted by missb

Hello,

I am new to this forum and am having difficulty with a particular question (I have searched for the answer, but have come up with nothing). Help is greatly appreciated

Question:

Determine the positions on the curve (x,y), of all tangents that pass through the point (2.53,25.34).

I really don't understand the question at all, so any help in working would be great.

Thanks in advance

Drawing a picture will help ....

At the point (a, b):

.... (1)

.... (2)

.... (3)

Solve these three equations simultaneously for a and b.

Thank you for the quick reply!

From my understanding, m is the first derivative of the original equation, m is usually how you calculate the slope in the form of right?

In your response, b is the original equation, so what is a? And do you use the quadratic formula to calculate a and b?

Sorry if this seems an obvious question, but I really just don't get it

Originally Posted by missb

Thank you for the quick reply!

From my understanding, m is the first derivative of the original equation, Mr F says: Correct.

m is usually how you calculate the slope in the form of [tex]m=\frac{y2-y1}{x2-x1}[\math] right? Mr F says: Correct. That's where equation (3) comes from.

In your response, b is the original equation, so what is a? Mr F says: (a, b) is the point on the curve that you're trying to find.

And do you use the quadratic formula to calculate a and b? Mr F says: If I was you, I'd substitute (1) into (3) and then equate (2) and (3). Now solve the resulting equation for a. etc.

Sorry if this seems an obvious question, but I really just don't get it

Draw a picture.