Chapter 5: Q. 3 (page 352)

Determine which of the following points are on the graph of $x^{2} + y^{2} = 1$ .
$(a) (\frac{1}{2}, \frac{1}{2}) (b) (\frac{1}{2}, \frac{\sqrt{3}}{2})$

Short Answer

Expert verified

Point $(\frac{1}{2}, \frac{1}{2})$ is not on the graph of $x^{2} + y^{2} = 1$
Point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ is on the graph of $x^{2} + y^{2} = 1$

Step by step solution

Part (a) Step 1. Given Information and Solution

We want to know the point $(\frac{1}{2}, \frac{1}{2})$ is on the graph or not.

The point $(\frac{1}{2}, \frac{1}{2})$ is on the graph if we in $x^{2} + y^{2} = 1$ instead of x and y include $x = \frac{1}{2} a n d y = \frac{1}{2}$ and we get a true statement.

So, for $x = \frac{1}{2} a n d y = \frac{1}{2}$ we get:

role="math" localid="1647322106882" $x^{2} + y^{2} = {(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2} = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}$

Since $\frac{1}{2} \neq 1$

We conclude that the point $(\frac{1}{2}, \frac{1}{2})$ is not on the graph of $x^{2} + y^{2} = 1$

Part (b) Step 1. Given Information and Solution

We want to know the point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ is on the graph or not.

The point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ is on the graph if we in $x^{2} + y^{2} = 1$ instead of x and y include $x = \frac{1}{2} a n d y = \frac{\sqrt{3}}{2}$ and we get a true statement.

So, for $x = \frac{1}{2} a n d y = \frac{\sqrt{3}}{2}$ we get:

role="math" localid="1647322123809" $x^{2} + y^{2} = {(\frac{1}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2} = \frac{1}{4} + \frac{3}{4} = 1$

Since $1 = 1$

We conclude that the point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ is on the graph of $x^{2} + y^{2} = 1$

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Determine which of the following points are on the graph of $x^{2} + y^{2} = 1$ .
$(a) (\frac{1}{2}, \frac{1}{2}) (b) (\frac{1}{2}, \frac{\sqrt{3}}{2})$

Short Answer

Step by step solution

Part (a) Step 1. Given Information and Solution

Part (b) Step 1. Given Information and Solution

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Short Answer

Step by step solution

Part (a) Step 1. Given Information and Solution

Part (b) Step 1. Given Information and Solution

One App. One Place for Learning.

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Determine which of the following points are on the graph of $x^{2} + y^{2} = 1$ .
$(a) (\frac{1}{2}, \frac{1}{2}) (b) (\frac{1}{2}, \frac{\sqrt{3}}{2})$