Introduction & Circles - Conic Sections (I)

I. Conic Sections INTRODUCTION & CIRCLES (Ch.10) I. VOCABULARY conic section the intersection of a plane and a double napped cone vertex an extreme point of a conic asymptote a line which a curve approaches locus the set of all points that satisfy an equation or condition focus a defining point of a conic nappe-half of a double cone directrix- adefining line of a conic II. BASIC CONICS double-napped cone circle parabola ellipse hyperbola III. CIRCLES (x-h)²+(y-k)² = r² center: (h,k) radius: r center a circle is a set of points (x,y) in a plane that are the same distance from a point called the center, (h,k) locus r radius (hk) Image Analysis Image Content: The image contains handwritten notes and diagrams related to parabolas. The content is organized into sections and includes definitions, equations, and visual representations of parabolas. Textual Content: II. Conic Sections PARABOLAS (Ch. 10) I. PARABOLAS a parabola is the set of all points (x,y) in a plane that are equidistant from a fixed line, the directrix, and a fixed point, the focus, not on the line.   \[x=h\] Taxis \[d_{y}\] focus d. \[(h,k+p)\] \[d_{2}|\] \[(x-h)^{2}=4p(y-k)\] \[d_{1}\] (n,k) vertex directrix \[y=k-p\] orientation opens vertically \[p>0\] vertex \((n,k)\) focus: \((h,k\cdot p)\) \[p<0\] axis \(x=h\) \[y=K-p\] directrix \(y=K-p\) \[(n,k)\] d, \[\phi_{z}\] \[\underline{d_{1}}\] \[(h,k+\vartheta)\] \[d_{2}\] \[x=h\] \[p>0\] \[P^{<}D\] \[d_{2}\] \[(y-k)^{2}=4p(x-h)\] \[d_{1}\] \[d_{2}\] orientationopens horizontally d focus axis vertex: \((h,k)\) \[(h+p_{i}k)\] (hk) [y=k.] \[y=k\] focus: \((h+p,k)\) \[(h,k)|\] \[(h+p,k)^{\prime}\] / \(d_{1}\) axis: \(y=k\) \[d_{1}\] directrix \(x=h-p\) \[d_{1}\] \[x=h-p\] \[d_{z}\] \[x=h-p\] locus locus directrix vertex