IzzyLJB
Badges: 7
Rep:
?
#1
Report Thread starter 2 years ago
#1
Any ideas on 4b? Thank you!
Attached files
0
reply
mqb2766
Badges: 18
Rep:
?
#2
Report 2 years ago
#2
Part a) must be a circle, radius 5, centered on (6,1).
Part b) Translates the origin to (11,10), then you have to find the smallest angle (most minimum) of a point on the circle from the new origin.
Can you sketch it?
0
reply
RDKGames
Badges: 20
Rep:
?
#3
Report 2 years ago
#3
(Original post by IzzyLJB)
Any ideas on 4b? Thank you!
\arg(z-(11+10i)) is a half-line starting from z_1 = 11+10i going off in some direction (blue line in my diagrams below)

The direction is limited though, because z must be on the circle that is defined by |z-6-i| = 5 (you sketch this circle in part a, it is the red one in my diagram).

Hence you are seeking for the minimum argument of the blue half-line (angle measured from the black dotted line in my diagram, labeled \theta) such that there is some intersection with the circle.

You need to look at two extremes. One of which is the following:


Spoiler:
Show


Image



or this one:

Spoiler:
Show


Image




Which one do you think represents the MINIMUM argument?? Work with that diagram and derive the answer for \theta.
0
reply
Mad Man
Badges: 16
Rep:
?
#4
Report 4 weeks ago
#4
Can anyone help me with part b ? I'm guessing the minimum arguement is pi/2 right? So where do I go from here?
0
reply
Mad Man
Badges: 16
Rep:
?
#5
Report 4 weeks ago
#5
I think I've got it please correct me if I'm wrong, or if I need to be more elaborate. See the attactched file.
Attached files
0
reply
mqb2766
Badges: 18
Rep:
?
#6
Report 4 weeks ago
#6
Looks good.
0
reply
Mad Man
Badges: 16
Rep:
?
#7
Report 4 weeks ago
#7
(Original post by mqb2766)
Looks good.
Is it worthy of full marks?
0
reply
Mad Man
Badges: 16
Rep:
?
#8
Report 4 weeks ago
#8
Pardon me, I forgot to put that sqrt(9^2 + 5^2)=sqrt(106)
0
reply
mqb2766
Badges: 18
Rep:
?
#9
Report 4 weeks ago
#9
(Original post by Mad Man)
Is it worthy of full marks?
It's a bit messy, but has the main points in. Hard for me to judge if you may be docked a mark.
For instance, you could describe why the two triangles are congruent, why the min angle corresponds to the tangent ... if you want to be guaranteed full marks. However, I don't have the mark scheme.
Last edited by mqb2766; 4 weeks ago
0
reply
Mad Man
Badges: 16
Rep:
?
#10
Report 4 weeks ago
#10
(Original post by mqb2766)
It's a bit messy, but has the main points in. Hard for me to judge of you may be docked a mark.
For instance, you could describe why the two triangles are congruent, why the min angle corresponds to the tangent ... if you want to be guaranteed full marks. However, I don't have the mark scheme.
I'm guessing we'd have to ask the OP IzzyLJB can you give the source of this question to me?
0
reply
mqb2766
Badges: 18
Rep:
?
#11
Report 4 weeks ago
#11
It is 2 years old and the OP hasn't logged on for several months. You've got the right method, so Id just move on?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Should there be a new university admissions system that ditches predicted grades?

No, I think predicted grades should still be used to make offers (727)
33.8%
Yes, I like the idea of applying to uni after I received my grades (PQA) (921)
42.82%
Yes, I like the idea of receiving offers only after I receive my grades (PQO) (408)
18.97%
I think there is a better option than the ones suggested (let us know in the thread!) (95)
4.42%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise