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Chapter 1: Q 10. (page 50)

Find the center and radius of the circle. Write the standard form of the equation.

Short Answer

Expert verified

Center is $(1, 2)$ .

Radius is $\sqrt{2}$ units.

Standard equation of a circle is $(x - 1)^{2} + (y - 2)^{2} = 2$ .

Step by step solution

01

Step 1. Given information

Figure is as follows:

02

Step 2. Find the center and radius of a circle.

Diameter is the distance between the points $(2, 3)$ and $(0, 1)$

Diameter $= \sqrt{(2 - 0)^{2} + (3 - 1)^{2}}$

$\begin{array}{rcl} = & \sqrt{4 + 4} \\ = & 2 \sqrt{2} \end{array}$

Center is the midpoint of the points $(2, 3)$ and $(0, 1)$

$\begin{array}{rcl} Center & = & (\frac{2 + 0}{2}, \frac{3 + 1}{2}) \\ = & (1, 2) \end{array}$

03

Step 3. Find the standard form of an equation of a circle.

Equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^{2} + (y - k)^{2} = r^{2}$

Therefore, equation of the circle with center $(1, 2)$ and radius $\sqrt{2}$ is

$(x - 1)^{2} + (y - 2)^{2} = (\sqrt{2})^{2}$

$(x - 1)^{2} + (y - 2)^{2} = 2$

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Most popular questions from this chapter

The points, if any, at which a graph crosses or touches the

coordinate axes are called ___________.

Find the midpoint of the line segment joining the points P₁ and P₂ .

$P_{1} = (- 2, 0); P_{2} = (2, 4)$

Which form of the equation of a line do you prefer to use? Justify your position with an example that shows that your choice is better than another. Have reasons.

The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph?

$(a) x - 2 y = 3 x + 2 y = 7 (b) x + y = 2 x + y = - 1 (c) x - y = - 2 x - y = 1 (d) x - y = - 2 2 x - 2 y = - 4 (e) x + 2 y = 2 x + 2 y = - 1$

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (3, 4)

See all solutions

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