# Help with Circle Geometry Homework - Calculate Co-ordinates of M

• DERRAN
In summary, the conversation discusses finding the coordinates of the point M, which lies on a circle with center (c,d) and also on the line 2x + 5y + 1=0. To find these coordinates, 3 equations are needed, which can be obtained by plugging in the given points (-1,6), (2,3), and (c,d) into the standard form of the equation for a circle. This results in the coordinates of M being (-3,1).
DERRAN

## Homework Statement

In the diagram alongside, A(2,3) and B(-1,6) lie on the circle with centre M(c,d).
M is also a point on the straight line defined by 2x + 5y + 1=0. The diagram is on the attached doc file.

Calculate the co-ordinates of M.

## Homework Equations

analytical methods only!

## The Attempt at a Solution

Im really stuck

#### Attachments

• Doc1.doc
24.5 KB · Views: 201
You have 3 unknowns (c, d, and the radius r of the circle), so you need 3 equations to find them. Try to answer the following questions. They should help you.

1.) What is the standard form of the equation form of a circle with center (c,d) and radius r?
2.) What do you get when you plug the point (x,y)=(-1,6) into that equation?
3.) What do you get when you plug the point (x,y)=(2,3) into that same equation?
4.) What do you get when you plug the point (x,y)=(c,d) into the equation of the given line?

That should get you started.

Tom Mattson said:
You have 3 unknowns (c, d, and the radius r of the circle), so you need 3 equations to find them. Try to answer the following questions. They should help you.

1.) What is the standard form of the equation form of a circle with center (c,d) and radius r?
2.) What do you get when you plug the point (x,y)=(-1,6) into that equation?
3.) What do you get when you plug the point (x,y)=(2,3) into that same equation?
4.) What do you get when you plug the point (x,y)=(c,d) into the equation of the given line?

That should get you started.

Thank you I got it. M is (-3,1)

## 1. What is circle geometry and why is it important?

Circle geometry is a branch of mathematics that studies the properties and relationships of circles. It is important because it has a wide range of real-world applications, such as in engineering, architecture, and navigation.

## 2. How do I calculate the coordinates of point M on a circle?

To calculate the coordinates of point M on a circle, you will need to know the radius of the circle and the angle formed by the radius and the x-axis. Using trigonometric functions, you can find the x and y coordinates of point M.

## 3. Can you provide an example of calculating the coordinates of M on a circle?

Sure, for example, if the radius of a circle is 5 units and the angle formed by the radius and the x-axis is 60 degrees, the coordinates of point M would be (2.5, 4.33).

## 4. Is there a specific formula for calculating the coordinates of M on a circle?

Yes, there is a formula for calculating the coordinates of point M on a circle, which is (x,y) = (r*cosθ, r*sinθ), where r is the radius of the circle and θ is the angle formed by the radius and the x-axis.

## 5. What are some common mistakes to avoid when calculating the coordinates of M on a circle?

Some common mistakes to avoid include using the wrong formula, forgetting to convert angles from degrees to radians, and not accounting for the signs of the coordinates. It is also important to double-check your calculations and use a calculator if necessary.

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