Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Total Exercises: 9
Type: Notes
| TITLE | SOLUTION |
|---|---|
| Exercise 6.1 | View |
| 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.