Maths Ext 1 Question (1 Viewer)

[Skeptyks]

Hey, just posted a thread but that was mathematics not maths ext 1 so I thought making a new thread would be appropriate.

In the figure, two tangents are drawn from the point to the curve . Find the equations of the two tangents. (Note that the point lies outside the curve)

Now, I have let the gradient of the tangent to be known as
The equation of the tangent is therefore, .
Expanding it out, .

Now I have the equations:

and

So,



Now, I am having a bit of trouble finding m...










Now, we multiply both sides by 16.

 

[freestyler1]

fuk off

 

[freestyler1]

cant you ask it at your matrix tutoring college.

 

[ohexploitable]

now find the equations, should be easy

 

[Skeptyks]

No, this is a question our teacher asked us to do. I don't go to a matrix tutoring college, whatever that is...

 

[freestyler1]

now find the equations, should be easy

hello smartass

 

[freestyler1]

No, this is a question our teacher asked us to do. I don't go to a matrix tutoring college, whatever that is...

well you should, its so cheap, gives you lots of false confidence too.

 

[FFBALLER]

umm just solve it for x but the discriminant is 0 because the tangents touch the graph from the point.
so b^2 - 4ac = 0

m^2 - 12m + 20 = 0

and find m,
which is 10 & 2?

 

[SpiralFlex]

For tangents,



Hence,









Now substitute back to ,

 

[ohexploitable]

now find the equations, should be easy

okay this probably needs a bit more explanation

gradient of any tangent is given by the derivative i.e. m=2x

but it's also must satisfy the condition of

so,

 

[Skeptyks]

For tangents,



Hence,









Now substitute back to ,

okay this probably needs a bit more explanation

gradient of any tangent is given by the derivative i.e. m=2x

but it's also must satisfy the condition of

so,

Understood Spirals but didn't understand yours exploitable sorry. Thanks to you both and FFballer ;].
BTW This freestyler1 and the nigga10 on the other thread is probably the same person... such a fail troll

 

[SpiralFlex]

Ohexploitable's method:

The derivative of is .

We can label this as . Hence also what you had,

So,



Substitute ,









Recall,



Hence,



Hence our equations are,

 

[Skeptyks]

Wow, that is a smarter/faster way to do it, thanks for the explanation.

 

[SpiralFlex]

Wow, that is a smarter/faster way to do it, thanks for the explanation.

Agreed. Happy to help. Please feel free to post any more questions.

 

[hscishard]

Alternatively...use parametrics[parabola part]

Parametrics suck...