Math 4 pair work on circles
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This document provides instructions for a pair work assignment on circles in mathematics. Students are asked to work in pairs to find the equations of circles given certain conditions in problems 1 through 7. Problems 8 through 10 require solving for specific values related to circles such as finding the value of k in an equation, the radius, or center of a circle. Students are to show their work and solutions on paper to turn in for the assignment.
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10.7 writing and graphing circles
The document discusses the standard form of the equation of a circle and how to find the center and radius from the equation. It provides examples of writing the equation given the center and radius, as well as finding the center and radius from an equation. Key aspects covered include:
- The standard form of a circle equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius
- Examples are worked through of writing the equation given the center and radius and vice versa
- Graphs are drawn to illustrate example circles
10.7 writing and graphing circles
The document discusses the standard form of the equation of a circle and how to find the center and radius from the equation. It provides examples of writing the equation given the center and radius, as well as finding the center and radius from an equation. Key aspects covered include:
- The standard form of a circle equation is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius
- You can find the center and radius by comparing the equation to the standard form
- Examples are worked through of writing equations given center and radius values and finding the center and radius from equations
Lesson 17: Quadratic Functions
The document discusses quadratic functions and parabolas. It defines a quadratic function as any function of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a ≠ 0. The graph of a quadratic function is called a parabola. Parabolas are symmetric and have an axis of symmetry, with a vertex point where the axis intersects the parabola. Standard and vertex forms for writing quadratic functions are presented, along with examples of finding the vertex and axis of symmetry from a given quadratic equation. Additional examples demonstrate how to graph parabolas and write the equation of a parabola given its graph.
Calculus a Functions of Several Variables
This document contains lecture notes on calculus of functions of several variables. It covers topics including vectors and vector spaces, geometry, vectors and the dot product, cross product, lines and planes in space, functions, vector valued functions, parameterized surfaces, parameterized curves, arc length and curvature. The notes provide definitions, examples, and exercises for each topic.
Polar Co Ordinates
This document provides an overview of 8 lessons on polar coordinates taught in a Further Pure Mathematics II course. The lessons cover key concepts such as plotting curves in polar form, converting between Cartesian and polar coordinates, determining maximum and minimum values of polar curves, finding equations of tangents, and calculating areas using polar coordinates. Practice problems are provided after each lesson covering the material through exercises and past exam questions.
1513 circles
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
May 19, 2014
The document provides information about topics to be covered in class today including warm-ups, make-up tests, reviews of radical equations, Pythagorean theorem, distance and midpoint formulas, and STAR testing. It then reviews solving radical equations, using the Pythagorean theorem, and applying the distance and midpoint formulas to different types of problems. Examples are provided for using the distance and midpoint formulas to find missing coordinates given certain known values.
D4 trigonometrypdf
The document discusses trigonometric functions and radians. It defines a radian as the angle subtended by an arc of a circle that is equal to the radius. A full circle is equal to 2π radians. The trigonometric functions can be defined using a unit circle in radians, allowing the description of periodic processes. Conversion between degrees and radians is covered. Polar coordinates are introduced as an alternative to Cartesian coordinates using radial distance and angle. Trigonometric identities and inverse functions are also discussed.
2.1 Rectangular Coordinate Systems
* Plot ordered pairs in a Cartesian coordinate system.
* Graph equations by plotting points.
* Find x-intercepts and y-intercepts.
* Use the distance formula.
* Use the midpoint formula.
May 15, 2014
The document provides information about reviewing radical operations, distance and midpoint formulas, and examples of using these formulas to solve problems. It includes:
- Examples of using the distance formula to find the distance between two points when all coordinates are known, and using three coordinates and the distance to find the unknown coordinate.
- The definition of a midpoint as the point halfway between the x-coordinates and y-coordinates of two endpoints.
- The midpoint formula for finding the x-coordinate and y-coordinate of the midpoint using the endpoints' coordinates.
- An example of using a known midpoint and one endpoint to find the other unknown endpoint.
ROOTS AND RADICALS - ELEMENTARY ALGEBRA
1. The document provides an overview of roots and radicals, including definitions of square roots, principal and negative square roots, radical expressions, rational and irrational numbers, and methods for simplifying, adding, subtracting, multiplying, dividing, and rationalizing radicals.
2. Square roots are factors whose product is the radicand, and the principal square root is the positive root. Radicals indicate roots and have a radicand and index. Rational numbers can be expressed as ratios while irrational numbers cannot.
3. Graphs and tables can be used to find approximate square roots. Radicals can be simplified using properties of exponents and fractions. Radical equations are solved by isolating the radical and taking squares of both
Circles
This document provides information about circles and their relationships to other geometric concepts:
1. It defines key concepts such as the distance formula, points on a circle, the equation of a circle with the center at the origin or other point (x,y), and the general equation of a circle.
2. It discusses the intersection of circles and lines, including finding the points of intersection using substitution and solving quadratics. The discriminant is used to determine the number of intersection points.
3. Tangents are defined as lines that intersect a circle at only one point and formulas are given for finding the equation of a tangent line to a circle.
9.2 - parabolas 1.ppt discussion about parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y=ax²+bx+c is a parabola if a≠0, and, conversely, a parabola is the graph of a quadratic function if its axis is parallel to the y-axis. The line perpendicular to the In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y=ax²+bx+c is a parabola if a≠0, and, conversely, a parabola is the graph of a quadratic function if its axis is parallel to the y-axis. The line perpendicular to the In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y=ax²+bx+c is a parabola if a≠0, and, conversely, a parabola is the graph of a quadratic function if its axis is parallel to the y-axis. The line perpendicular to the In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic s
Rank nullity theorem
The Rank-Nullity Theorem states that for any matrix A, the dimension of A's row space equals the dimension of its column space. The rank of A is defined as the dimension of its row space, while the nullity is the dimension of A's null space. The theorem also states that for any m×n matrix A, the rank plus the nullity equals the number of columns n.
Similar to Math 4 pair work on circles (20)
Math 4 pair work on circles
- 1. Pair Work on Circles Mathenlatics 4 Second Quarter .. August 8, 2010 Vork on this problem set by pairs. Answers and complete solutions should be printed or written on Letter or A4 size white paper. Work with a different partner from the first, pair work. . For numbers 1 to 7, find the equation of the circle(s) satisfying the given conditions: (3 points each) . For numbers 8 to 10, solve each problem as specified. (4 points each) 1. Center at (3, -1) and passes through the point (-2,2). 2. Has a diameter whose endpoints are (-2,4) and (4,2). 3. Center at (5, -2), the midpoint of the segment joining the center and one of the points on the circle is (-2,1). 4. Passes through P(5, -4) with R( - , -8) being the point ~ of the way from the center to P. 5. Passes through t.he points (-1,0), (0,2), and (2,0). (Use syst.ems of equations) 6. PaR"IeS through the points (-4,-3)' (-2,1), and (-:3,-6). (Use analytic geomet.ry) 7. Radius is 2 and passing through the points (1,2) and (:1,4). 8. The circle x 2 + y2 + 4x -- 6y k passes through the point (-1,-1). Find the value of k, the radius, and the center of the circle. 9. For what values of rand .9 will x 2 + y2 + 'rx + sy 25 0 be the equation of a circle having center at. (3A)? Fiud the radius of this cirde. 10. Determine the value(s) of kso that the graph of 2 k 2 4k 110 + y + 2:z:: - 4y = - - - 2 - is a circle, a point, or an empty set.