Chapter 6 (Conic Section) FSc Part 2 Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Total Exercises: 9
Type: Notes

TITLESOLUTION
Exercise 6.1View
Exercise 6.2 View
Exercise 6.3 View
Exercise 6.4 View
Exercise 6.5 View
Exercise 6.6 View
Exercise 6.7 View
Exercise 6.8 View
Exercise 6.9 View

In this chapter we will read these topics:

  • Define cone, vertex of cone and axis of cone.
  • Define nappes of cone and types of cone.
  • Define Conic or Conic section.
  • Define Circle.
  • Define Point Circle.
  • Define Ellipse.
  • Define Parabola.
  • Define Hyperbola.
  • What is the difference between the diameter and chord of a circle?
  • Derive the standard equation of circle.
  • Find the equation of circle having center at origin and radius r.
  • Find the parametric equation of circle having radius r and center at origin.
  • When two circles touch each other externally.
  • When two circles touch each other internally.
  • Tangent to a circle is perpendicular to radius.
  • Tangents and normals.
  • Define tangent and normal to a curve.
  • Find equation of tangent and normal to circle.
  • Normal line is perpendicular to the line.
  • Condition of tangency.
  • Tangential distance.
  • Equation of chord of contact.
  • Analytic proofs of important properties of circle.
  • Perpendicular dropped from the center of a circle on a chord bisects the chord.
  • The perpendicular bisector of any chord of a circle passes through the center of the circle.
  • The line joining the center of a circle to the mid-point of a chord is perpendicular to the chord.
  • The slope of chord.
  • Congruent chords of a circle are equidistance from center.
  • Show that the measure of the central angle of minor arc is double the measure of the angle subtended in the corresponding major arc.
  • An angle in a semi-circle is a right angle.
  • The tangent to a circle at any point of the circle is perpendicular to the radial segment at that point.
  • Perpendicular at outer end of a radial segment is tangent to circle.
  • Define parabola.
  • Derive the standard equation of parabola y2=4ax.
  • Derive the general equation of a parabola.
  • Write the relationship between the second-degree equation and parabola.
  • Define focus, directrix, axis and vertex of parabola.
  • Define tangent at vertex and chord of parabola.
  • Define the focal chord and latus rectum of the parabola.
  • What do you mean by the eccentricity of a parabola?
  • Prove that length of latus rectum of a parabola is 4a.
  • Point of a parabola which is closest to the focus is the vertex of parabola.
  • Length of latus rectum.
  • Define Reflecting property of parabola.
  • Define ellipse.
  • The fixed point is called the focus.
  • Define the diameters of an ellipse.
  • Define major axis of an ellipse and length of major axis.
  • Define minor axis of an ellipse and length of minor axis.
  • Define directrices of an ellipse.
  • Define the Foci of an ellipse.
  • Define vertices of an ellipse.
  • Define co-vertices of an ellipse.
  • Define chord of an ellipse.
  • Define focal chord of an ellipse.
  • Define latus rectum and length of latus rectum of an ellipse.
  • Define center of an ellipse.
  • Define semi-major axis and semi-minor axis of an ellipse.
  • Write the parametric equations of an ellipse.
  • Derive the equation of directrix of an ellipse.
  • Define hyperbola.
  • Define center of Hyperbola.
  • Define focal axis or transvers axis of Hyperbola.
  • Define the conjugate axis of Hyperbola.
  • Define the vertices of Hyperbola.
  • What is length of latus rectum of Hyperbola?
  • Write the parametric equation of Hyperbola.
  • Which conics re called conics.
  • Discuss the sketch graph of the equation.
  • Tangents and normals.
  • Condition of tangency.
  • Find the point of intersection ellipse and hyperbola.
  • Find the point of intersection of conics.
  • Define the translation of axes.
  • Write the equation of the translation of axes.
  • Define the rotation of axes.
  • Write the equation of rotation of axes.
  • Transformed equation.
  • Define the general equation of second degree.
  • When the general equation of second degree represents a circle.
  • When the general equation of second degree represents a parabola.
  • When the general equation of second degree represents a ellipse.
  • When the general equation of second degree represents a hyperbola.
  • Classification of conics by discriminant.
  • Discuss the nature of conics.
  • What is degenerate conic?
  • Elements of the ellipse.
  • Equation of major axis.
  • Equation of minor axis.
  • Equation of transformation.
  • Elements of the hyperbola.
  • Equation of focal axis.
  • Equation of the conjugate axis.

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