Conic Section Class 12 Mathematics Notes has been updated according to the latest syllabus of 2080. It means the notes of Conic Section chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.
Chapter – 8
Conic Section
Parabola is a symmetrical curve formed by the set of points that are equidistant from a fixed point (focus) and a fixed straight line (directrix). This U-shaped curve is a fundamental shape in mathematics and physics, with applications in various fields.
Properties of Parabola
- Focus and Directrix: The focus is a fixed point on the axis of symmetry, and the directrix is a fixed straight line perpendicular to the axis of symmetry.
- Vertex: The midpoint between the focus and the directrix is known as the vertex, which lies on the axis of symmetry.
- Axis of Symmetry: A line passing through the vertex and perpendicular to the directrix is called the axis of symmetry.
Conic Section Class 12 Mathematics Notes PDF
This PDF will provide the solutions of every question from the 3rd exercise of class 12 conic section which contains the exercise related to parabola. If you want the solutions of other exercises then you can select the exercise from the button given above.
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Condition of Tangents to a Parabola
The condition for a straight line to be a tangent to a parabola involves the line touching the curve at exactly one point. This occurs when the line is perpendicular to the parabola’s axis of symmetry at the point of contact. The slope of the tangent line at the point of contact is equal to the derivative of the parabola’s equation at that point.
Applications of Parabola
- Optics: Parabolic mirrors and lenses are used to focus light in telescopes, satellite dishes, and headlights.
- Projectile Motion: The path of a projectile under gravity follows a parabolic trajectory.
- Engineering: Parabolic shapes are utilized in designing antennas, satellite dishes, and reflectors for various applications.
Understanding the properties and characteristics of parabolas, along with the conditions for tangents to straight lines, is essential for solving problems involving these curved shapes in mathematics and various real-world applications.
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