Ch 10 studies curves obtained by slicing a cone: circles, parabolas, ellipses, and hyperbolas. Students derive standard equations and learn to identify, graph, and analyse these curves.
Standard equation: (x−h)² + (y−k)² = r² with centre (h,k) and radius r. General form: x² + y² + 2gx + 2fy + c = 0 with centre (−g,−f) and radius √(g²+f²−c).
The locus of a point equidistant from a fixed point (focus) and a fixed line (directrix). Standard forms: y²=4ax (opens right), y²=−4ax (left), x²=4ay (up), x²=−4ay (down). Vertex at origin.
Ellipse: x²/a² + y²/b² = 1 with foci (±c,0), c² = a²−b². Eccentricity e = c/a < 1. Hyperbola: x²/a² − y²/b² = 1 with foci (±c,0), c² = a²+b². Eccentricity e = c/a > 1.
Download: https://ncert.nic.in/textbook/pdf/kemh110.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
Eccentricity (e): circle (e=0), ellipse (0 < e < 1), parabola (e = 1), hyperbola (e > 1). It measures how "stretched" the curve is from a circle. Alternatively, the angle of the cutting plane relative to the cone determines the type.
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