Tiêu đề LECTURE NOTES DAY 09_ ANALYTIC GEOMETRY 2.pdf ✅

DAY 9: ANALYTIC GEOMETRY 2 LECTURE OUTLINE • Conic Sections – Circles • Conic Sections – Ellipses • Conic Sections – Parabolas • Conic Sections – Hyperbolas • General Conic Sections Believe you can and you are halfway there.
DAY 9: ANALYTIC GEOMETRY 2 CONIC SECTIONS - CIRCLES Believe you can and you are halfway there. A circle is the locus of points equidistant to a point called the center. For a point (x, y) centered at (h, k) with radius r, x − h 2 + y − k 2 = r 2 This equation is called the center-radius form.
DAY 9: ANALYTIC GEOMETRY 2 CONIC SECTIONS - CIRCLES Believe you can and you are halfway there. Expanding the center-radius form, x 2 − 2hx + h 2 + y 2 − 2yk + k 2 = r 2 x 2 + y 2 − 2hx − 2ky + h 2 + k 2 − r 2 = 0 Let D = −2h,E = −2k, and F = h 2 + k 2 − r 2 , x 2 + y 2 + Dx + Ey + F = 0 This form is called the standard equation of a circle.