Solution of Past Paper of CAIE Math 9709/12 Feb/Mar 2020 Question # 12
4 views 0 purchase
Course
CAIE AS & A Level Mathematics P1 (9709/1)
Institution
CAIE AS & A Level Mathematics P1 (9709/1)
This document presents most carefully worked out and thoroughly explained complete Solution of Past Paper of Cambridge AS/A Level Mathematics (9709), Pure Mathematics 1, Feb/March 2020
We also provide on-on-one online help for students who still need some help beyond our provided solution.
We al...
solution of past paper 9709 12 february march 2020
Written for
CAIE AS & A Level Mathematics P1 (9709/1)
All documents for this subject (23)
Seller
Follow
hummairamubashar
Content preview
CIE/GCE/AS/Math/P1/20/Mar/12/Q#12
Question
A diameter of a circle C1 has end-points at (−3, −5) and (7, 3).
a) Find an equation of the circle C1.
8
The circle C1 is translated by ( ) to give circle C2, as shown in the diagram.
4
b) Find an equation of the circle C2.
The two circles intersect at points R and S.
c) Show that the equation of the line RS is y = −2x + 13.
d) Hence show that the x-coordinates of R and S satisfy the equation
5x2 − 60x + 159 = 0
Solution
a)
, CIE/GCE/AS/Math/P1/20/Mar/12/Q#12
We are given that points at (−3, −5) and (7, 3) makes end-points of the diameter of a
circle C1.
If coordinates of end points of diameter, 𝐴 and 𝐵 are given;
✓ Find the coordinates of mid-point of 𝐴𝐵, this gives coordinates of center of the
circle 𝐶(𝑎, 𝑏)
✓ Find the distance 𝐶𝐴 or 𝐶𝐵 , this gives the radius of the circle 𝑟
✓ Use the equation of the circle (𝑥 − 𝑎)2 + (𝑦 − 𝑏)2 = 𝑟 2
Therefore, first we find the midpoint of given end-points A(−3, −5) and B(7, 3) of
diameter of the circle C1.
To find the mid-point of a line we must have the coordinates of the end-points of the
line.
Expressions for coordinates of mid-point of a line joining points 𝑃1 (𝑥1 , 𝑦1 ) and𝑃2 (𝑥2 , 𝑦2 );
1
x-coordinate of mid-point 𝑀(𝑥, 𝑦) of the line= 𝑥𝑀 = (𝑥1 + 𝑥2 )
2
1
y-coordinate of mid-point 𝑀(𝑥, 𝑦) of the line= 𝑦𝑀 = (𝑦1 + 𝑦2 )
2
Hence;
1 1 1
x-coordinate of mid-point 𝐶(𝑥, 𝑦) of the line= 𝑥𝐶 = 2 (𝑥𝐴 + 𝑥𝐵 ) = 2 (−3 + 7) = 2 (4) = 2
1 1 1
y-coordinate of mid-point 𝐶(𝑥, 𝑦) of the line= 𝑦𝐶 = 2 (𝑦𝐴 + 𝑦𝐵 ) = 2 (−5 + 3) = 2 (−2) = −1
Hence, the point 𝐶(2, −1) is the center of the circle 𝐶1 .
Next, we find the radius of the circle 𝐶1 by finding either distance CA or CB.
We choose to find CB.
Expression to find distance between two given points 𝐴(𝑥𝐴 , 𝑦𝐴 ) and 𝐵(𝑥𝐵 , 𝑦𝐵 )is:
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller hummairamubashar. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.99. You're not tied to anything after your purchase.
