circles

Question 1

possible questions

Answer 1

• equation of a circle
• intersection of line and circle
• equation of a tangent to a circle
• intersection of two circles
• checking if a point lies in/on/outside a circle
• checking if something is a circle
• find co-ords where 2 circles intersect
• congruent and concentric circles

Question 2

equation of a circle steps

Answer 2

Q: find equation of circle with radius 6 and centre (-4,1)
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* (x-a)² + (x-b)²=r²
* (x-(-4))² + (x-1)²= 6²
* (x+4)² + (x-1)²= 36

Question 3

equation of a circle without the centre or radius steps

Answer 3

Q: find the equation with AB as a diameter A(-2, -7) B(0, 3)
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* find centre with midpoint
(-2, -7) (0, 3)= (-1, -2)
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* radius with distance formula
√(x2-x1)² + (y2-y1)²
√(-2-(-1))² + (-7-(-2))²
√(-1)² + (-5)²
√26
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* equation
(x-a)² + (x-b)²=r²
(x-(-1))² + (x-(-2))²= (√26)²
(x+1)² + (x+2)²= 26

Question 4

intersection of line and circle process

Answer 4

• sub y of line into circle
• simplify alike terms to ax²+bx+c
• factorise and find roots
• statement of what roots mean (=0, >0, <0)

Question 5

equation of tangent to a circle process

Answer 5

• find centre of circle
• gradient using centre then (a,b)
• m1xm2= -1
• equation

Question 6

intersection of two circles process

Answer 6

• find radius and centre of both circles
• distance formula with both centres
• statement with comparison of radii added together and distance
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  possible statements
  R1+R2=d , R1+R2>d , R1+R2<d

Question 7

checking if a point lies in/on/outside a circle steps

Answer 7

• sub co-ord into circle equation
• statement that determines where the point lies

possible statements
LHS=RHS , LHS>RHS , LHS<RHS

Question 8

checking if something is a circle

Answer 8

• find radius and centre of equation
• if radius is a minus, radius not real, and neither is circle

Question 9

what is a congruent circle?

Answer 9

circles that have the same radius

Question 10

what is a concentric circle?

Answer 10

circles that have the same centre

(same radius, diameter or circumferance)

Question 11

how do you calculate the circumferance of a circle?

Answer 11

2πr

Question 12

how do you find the co-ords of where 2 circles intersect

Answer 12

• check if they are on the same x or y axis
• if so, check where the side co-ord lies

e.g if c1=r6 and c2=r3 and share an x/y co-ord
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(OR)
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synthetic division