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Circles and Parabolas, SMB-018

  1. Find the centre and radius of the circle with the equation
  2.      `x^2-2x+y^2+3y-3/4=0`  (2 marks)

  3. Sketch the circle on the graph below.  (1 mark)
     

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a.   `text{Centre}\ (1,-3/2),\ \ text{Radius}\ =2`

b.  


        

Show Worked Solution
a.    `x^2-2x+y^2+3y-3/4` `=0`
  `x^2-2x+1+y^2+3y+9/4-4` `=0`
  `(x-1)^2+(y+3/2)^2` `=2^2`

 
`text{Centre}\ (1,-3/2),\ \ text{Radius}\ =2`

b.   

 

Circles and Hyperbolas, SMB-017

  1. Find the centre and radius of the circle with the equation
  2.      `x^2-4x+y^2+6y+9=0`  (2 marks)

  3. Sketch the circle on the graph below.  (1 mark)

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a.   `text{Centre}\ (2,-3),\ text{Radius}\ = 2`

b.   


        

Show Worked Solution
a.    `x^2-4x+y^2+6y+9` `=0`
  `x^2-4x+4+y^2+6y+9-4` `=0`
  `(x-2)^2+(y+3)^2` `=2^2`

  
`:.\ text{Centre}\ (2,-3),\ text{Radius}\ = 2`

b.   

Circles and Hyperbolas, SMB-014

  1. Find the centre and radius of the circle with the equation
  2.      `x^2+6x+y^2+4y+4=0`  (2 marks)

  3. Sketch the circle on the graph below.  (1 mark)
     

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a.   `(x+3)^2 + (y+2)^2 = 3^2`

`:.\ text(Centre:)\ (-3,-2)\text(, Radius:)\ 3`

b.   

Show Worked Solution
a.    `x^2+6x+y^2+4y+4` `=0`
  `x^2+6x+9+y^2+4y+4-9` `=0`
  `(x+3)^2+(y+2)^2` `=3^2`

  
`:.\ text(Centre:)\ (-3,-2)\text(, Radius:)\ 3`

  
b.   

Circles and Hyperbolas, SMB-013

  1. Write down the equation of the circle with centre `(1, -2)` and radius 2.  (1 mark)

  2. On the graph, sketch the circle in part (a).  (2 marks)

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a.   `(x-1)^2 + (y+2)^2 = 4`

b.    
     

Show Worked Solution

a.   `text{Circle with centre}\ (1,-2),\ r = 2:`

`(x-1)^2 + (y+2)^2 = 4`
 

b.   

Functions, 2ADV F1 2016 HSC 11a

Sketch the graph of  `(x-3)^2 + (y + 2)^2 = 4.`  (2 marks)

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Show Worked Solution

`(x-3)^2 + (y + 2)^2 = 4\ \ text(is a circle),`

`text(centre)\ (3, -2),\ text(radius 2.)`