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

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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