CEMC's Open Courseware - Lesson 4: Equation of a Circle

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- Watch and Read
- - Let's Start Thinking
  - Equation of a Circle Centred at \((0,0)\)
  - Equation of a Circle Centred at \((h,k)\)
  - Wrap-Up
  - Extension
  - Alternative Format
- Review
- - Explore This 1
  - Check Your Understanding 1
  - Check Your Understanding 2
  - Check Your Understanding 3
- Practise
- - Exercises
  - Answers
  - Solutions

Exercises

1. Determine an equation of a circle with a radius of \(\)\(3\) and centered at \((0,0)\).
2. Determine an equation of a circle with a diameter of \(16\) and centered at \((0,0)\).
1. Determine an equation of a circle with a radius of \(5\) and centered at \((-4,-7)\).
2. Determine an equation of a circle with a diameter of \(8\) and centered at \((-1,2)\).
Determine an equation of a circle centered at \((-13,-16)\) with the point \((-10,-16)\) on its circumference.
Determine an equation of a circle with a diameter that has endpoints at \((18,-13)\) and \((4,-3)\).
A park is in the shape of a circle that is represented by the equation \(x^2+y^2=64\). The park was designed to have a circular rose garden at the centre, concentric with the park and represented by the equation \(x^2+y^2=16\). Determine the area of the park that does not contain roses.
A rabbit will move no more than \(10\) m away from its hole.
At a given time, you are taking a walk \(5\) m east and \(\)\(7\) m north of the rabbit hole.

Is there any possibility of you meeting up with the rabbit?
A ship drops its anchor into the water and creates a circular ripple. The radius of this ripple increases at a rate of \(50\) m/s.
1. Determine an equation of the circle \(10\) s after the anchor is dropped.
2. A small rowboat is \(50\) m west and \(75\) m south of the point the anchor was dropped. How long will it take the ripple to reach the boat?
The epicenter of an earthquake is the location on the earth's surface directly above where the earthquake originated. A seismograph measures the distance to the epicenter of an earthquake. Readings from seismographs in three different places are used to locate the epicenter of an earthquake.
The following readings from a specific earthquake were recorded:
- Seismograph 1: epicenter \(4\) km away from \((1,4)\)
- Seismograph 2: epicenter \(5\) km away from \((-6,0)\)
- Seismograph 3: epicenter \(10\) km away from \((5,-2)\)
Given these three recordings, where is the epicenter of the earthquake?
1. Determine the radius of the circle represented by the equation \(x^2+y^2+2x+6y-15=0\).
2. Determine the diameter of the circle represented by the equation \(x^2+y^2+10x-14y-7=0\).
3. Determine the centre of the circle represented by the equation \(3x^2+3y^2-12x-24y+12=0\).