3. Functions and Graphs

Find the Distance Between Two Points

Distance and Midpoint Formulas; Circles

The Distance Formula - Deriving the Formula from Pythagorean Theorem

Finding the Center-Radius Form of a Circle by Completing the Square - Example 2

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x+3)² + (y + 2)² = 4

In Exercises 67–70, graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. x² + y² = 16, x-y = 4

Radius and center for a circle equation in standard form | Algebra II | Khan Academy

Finding Endpoint Given Midpoint

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x + 2)² + (y - 2)² = 4

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x − 3)² + (y + 1)² = 36

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+3x+5y+9/4=0

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² - 2x + y² – 15 = 0

The Distance Formula: Finding the Distance Between Two Points

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-1/4, -1/7) and (3/4, 6/7)

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (0, 0), r = 7

Find the center and radius of a circle

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-2, -8) and (−6, −2)

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (6, 8) and (2, 4)

Midpoint of Two Points - Another Example

Translate the equation of a circle from general form to standard form

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6

Understand the standard form equation for circles

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² – 10x – 6y – 30 = 0

Find the distance between points using the distance formula

The Distance Formula and Finding the Distance Between Two Points - Example 2

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (√50, −6) and (√2, 6)

In Exercises 65-66, a line segment through the center of each circle intersects the circle at the points shown.
a. Find the coordinates of the circle's center.
b. Find the radius of the circle.
c. Use your answers from parts (a) and (b) to write the standard form of the circle's equation. <p><img src="https://lightcat-files.s3.amazonaws.com/problem_images/546ad3f74cffae60-1674572751928.jpg" alt="" /></p><p><img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/09c383228804e34c-1678171948303.jpg" style="width: 300px;"></p>

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (4, -1) and (-6, 3)

In Exercises 109–111, give the center and radius of each circle. x^2 + y^2 - 4x + 2y - 4 = 0

Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7, 2) and (x2, y2) = (1, −1). Find √[(x2 − x1)² + (y2 − y₁)²]. Express the - answer in simplified radical form.

Finding the Center-Radius Form of a Circle by Completing the Square - Example 3

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+8x-2y-8=0

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² - 6y -7=0

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² − x + 2y + 1 = 0

How To Find The Midpoint Using The Midpoint Formula

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)

The Center-Radius Form for a Circle - A few Basic Questions, Example 2

Finding the Center-Radius Form of a Circle by Completing the Square - Example 1

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. (x + 1)² + y² = 25

How to do the Distance Formula

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (2, 3) and (14, 8)

Graphing Conic Sections Part 1: Circles

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. x² + (y − 1)² = 1

The Distance Formula and Finding the Distance Between Two Points - Example 1

How to do the Midpoint Formula 

In Exercises 105–106, find the midpoint of each line segment with the given endpoints. (2, 6) and (-12, 4)

The Center-Radius Form for a Circle - A few Basic Questions, Example 1

In Exercises 67–70, graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. (x − 2)²+(y+3)² = 4, y = x - 3

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)

The Midpoint Formula

Finding Midpoint AND WALDO!!!

Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

In Exercises 49–56, identify each equation without completing the square.

4x^2 + 4y^2 + 12x + 4y + 1 = 0

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3.5, 8.2) and (-0.5, 6.2)

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, −√3) and (√5, 0)

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation’s domain and range. x² + y² = 16

Exercises 103–105 will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3√3, √5) and (−√3, 4√5)

The Midpoint Formula - Finding the Midpoint

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (−3, −1), r = √3

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (3, 2), r = 5

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, 0) and (3,-4)

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (8, 3√5) and (−6, 7√5)

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (-4, 0), r = 10

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+6x+2y+6 = 0

Find the center and radius of a circle by completing the square

Write the equation of a circle centered at (h, k)

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (-1, 4), r = 2

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, -√2) and (√7,0)

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (7√3, −6) and (3√3, −2)

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (7/3, 1/5) and (1/3, 6/5)

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