# Thread: Tangent passes through a particular point.

1. ## 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:

$y= -3x^2 - 6.14$ 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.

2. 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:

$y= -3x^2 - 6.14$ 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.

Drawing a picture will help ....

At the point (a, b):

$b = -3a^2 - 6.14$ .... (1)

$m = \frac{dy}{dx} = -6a$ .... (2)

$m = \frac{b - 25.34}{a - 2.53}$ .... (3)

Solve these three equations simultaneously for a and b.

3. 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 $m=\frac{y2-y1}{x2-x1}$ 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

4. 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.