1 / 9

CIRCLES

CIRCLES. SPECIFIC OBJECTIVES: At the end of the lesson, the student is expected to be able to: • draw a circle given different points. • determine center and radius of the circle given an equation.

Albert_Lan
Télécharger la présentation

CIRCLES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. CIRCLES

  2. SPECIFIC OBJECTIVES: At the end of the lesson, the student is expected to be able to: • draw a circle given different points. • determine center and radius of the circle given an equation. • determine general and standard form of equation of the circle given some geometric conditions. • convert general form to standard form of equation of the circle and vice versa.

  3. CIRCLE A circle is a locus of points that moves in a plane at a constant distance from a fixed point. The fixed point is called the center and the distance from the center to any point on the circle is called the radius. Parts of a Circle Center - It is in the centre of the circle and the distance from this point to any other point on the circumference is the same. Radius - The distance from the centre to any point on the circle is called the radius. A diameter is twice the distance of a radius. Circumference - The distance around a circle is its circumference. It is also the perimeter of the circle

  4. Chord - A chord is a straight line joining two points on the circumference. The longest chord in a called a diameter. The diameter passed through the centre. Segment - A segment of a circle is the region enclosed by a chord and an arc of the circle. Secant - A secant is a straight line cutting at two distinct points. Tangent - If a straight line and a circle have only one point of contact, then that line is called a tangent. A tangent is always perpendicular to the radius drawn to the point of contact.

  5. Equation of a Circle

  6. Let: C (h, k) - coordinates of the center of the circle r - radius of the circle P (x, y) - coordinates of any point along the circle From the figure, Distance CP = radius ( r ) Recall the distance formula: Squaring both sides of the equation, r2 = (x – h)2 + (y – k)2 The equation is also called the center-radius form or the Standard Form. (x – h)2 + (y – k)2 = r2

  7. If the center of the circle is at the origin (0, 0) h = 0 k = 0 C (h, k) C (0, 0) From (x – h)2 + (y – k)2 = r2 (x – 0)2 + (y – 0)2 = r2 x2 + y2 = r2 Center at the origin

  8. From (x – h)2 + (y – k)2 = r2 Standard Form Center at (h, k) (x2 – 2hx + h2) + (y2 – 2kx + k2) = r2 x2 + y2 – 2hx – 2ky + h2 + k2 + r2= 0 Let: 2h = D 2k = E CONSTANTS h2 + k2 + r2 = F Therefore, x2 + y2 + Dx + Ey + F = 0General Form

  9. Examples: If the center of the circle is at C(3, 2) and the radius is 4 units, find the equation of the circleand sketch the graph. Reduce to standard form and draw the circle whose equation is 4x2 + 4y2 – 8x – 8y – 16 = 0. Determine the center and radius of the circle (x + 3)2 + (y – 2)2 = 16. Sketch the graph. Reduce x2+ y2– 18x + 10y + 25 = 0 to the center-radius form of the circle. Give the standard form for the equation of a circle with center (2, –4) and radius 5. Find the equation of the circle having (–1, –3) and (7, –1) as ends of a diameter.

More Related