Finding the Centre of a Circle Passing Through Given Points (1,-2) and (4,-3)

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In summary, the centre of a circle is the point in the exact middle of the circle, equidistant from all points on the circumference. It can be found by drawing two diameters and finding their intersection. The centre is always located inside the circle and a circle can only have one centre. The centre is important in geometry as it helps define and construct other elements of a circle and is used in various theorems and formulas.
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Homework Statement


Find the centre of the circle which passes through the points (1,-2) and (4,-3) whose centre lies on the line 3x + 4y = 7


Homework Equations





The Attempt at a Solution



distance from the centre of the circle to the given points is equal
by distance formula and simplifying,
I got 3x-2y=10

On Solving 3x + 4y= 7 and 3x - 2y= 10
I got the point (3,-1/2) as the centre of the circle.
But answer is something else.
Please help
 
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  • #2
I get as a second equation
[tex] 3x -y=10[/tex]
 
  • #3
Damn! such a silly mistake
Thanks mate.
 

FAQ: Finding the Centre of a Circle Passing Through Given Points (1,-2) and (4,-3)

1. What is the definition of the "centre of a circle"?

The centre of a circle is the point in the exact middle of the circle. It is equidistant from all points on the circle's circumference.

2. How do you find the centre of a circle?

To find the centre of a circle, you can draw two diameters (lines that pass through the centre and divide the circle into two equal halves) and the point where they intersect is the centre.

3. Is the centre of a circle always located inside the circle?

Yes, the centre of a circle is always located inside the circle. This is because the radius (the distance from the centre to any point on the circle) is always shorter than the diameter (the distance across the circle through the centre).

4. Can a circle have more than one centre?

No, a circle can only have one centre. This is a defining characteristic of a circle - all points on the circumference must be equidistant from the centre. If more than one point were the centre, this would not be true.

5. What is the importance of the centre of a circle in geometry?

The centre of a circle is important in geometry because it is used to define and construct other important elements of a circle, such as the radius, diameter, and circumference. It is also used in various theorems and formulas related to circles, such as the Pythagorean theorem and the formula for the area of a circle.

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