How Do You Determine If a Point Lies on a Circle?

[mathdad]

1. Sketch the circle of radius 1 centered at (0, 0).

(A) Write the equation of this circle.

I must use x^2 + y^2 = r^2.

The radius is 1. This means r = 1.

The equation is x^2 + y^2 = 1. Correct?

B. Does the point (3/5, 4/5) lie on this circle?

(3/5)^2 + (4/5)^2 = 1^2

(9/25) + (16/25) = 1

(9 + 16)/25 = 1

25/25 = 1

1 = 1

I say yes. Right?

 

[Greg]

1. Sketch the circle of radius 1 centered at (0, 0).

(A) Write the equation of this circle.

I must use x^2 + y^2 = r^2.

The radius is 1. This means r = 1.

The equation is x^2 + y^2 = 1. Correct?

Correct.

B. Does the point (3/5, 4/5) lie on this circle?

(3/5)^2 + (4/5)^2 = 1^2

(9/25) + (16/25) = 1

(9 + 16)/25 = 1

25/25 = 1

1 = 1

I say yes. Right?

Right. Good work!

 

[mathdad]

Good to know that I am right.

 

[Greg]

B. Does the point (3/5, 4/5) lie on this circle?

(3/5)^2 + (4/5)^2 = 1^2

(9/25) + (16/25) = 1

(9 + 16)/25 = 1

25/25 = 1

1 = 1

In the first and following lines above, you are assuming what you are trying to show. The above can be properly written as

$$\left(\frac35\right)^2+\left(\frac45\right)^2=\frac{9}{25}+\frac{16}{25}=\frac{9+16}{25}=\frac{25}{25}=1$$

:)

 

[mathdad]

In the first and following lines above, you are assuming what you are trying to show. The above can be properly written as

$$\left(\frac35\right)^2+\left(\frac45\right)^2=\frac{9}{25}+\frac{16}{25}=\frac{9+16}{25}=\frac{25}{25}=1$$

:)

Isn't that what I did?