Скачать или смотреть Exercise 7.5 class 12 math | NBF FBISE new book 2025 | ex 7.5 12th class math |Parabola by Dr Rizwan

Exercise 7.5 Class 12 Math || NBF New Book 2025 || Conic Section Chapter 7 || Complete Tangent, Normal & Focal Chord Concepts || by Dr Rizwan

In this lecture, we provide a complete, conceptual, exam-oriented discussion and step-by-step solution of Exercise 7.5 from Class 12 Mathematics (National Book Foundation – NBF 2025 Edition), prescribed by FBISE (Federal Board), Islamabad.

Exercise 7.5 is the heart of the parabola chapter — covering the most important geometric tools: line–parabola intersection, tangency conditions, parametric points, focal chords, orthogonality, and directrix-based theorems.

⏱️ Timestamp Overview
00:00:00 Introduction
‎00:06:52 Question 01
‎00:22:53 Question 02
‎00:29:51 Question 03
‎00:38:50 Question 04
‎00:45:53 Question 05
‎00:51:55 Question 06
‎00:56:47 Question 07
‎01:06:08 Question 08
‎01:16:34 Question 09
‎01:31:11 Question 10
01:47:31 Question 11
01:55:40 Question 12

📌 Core Concepts Explained
✔️ Line–Parabola Intersection
✔️Condition for two distinct intersection points
✔️When the line becomes parallel and gives no intersection
✔️When the line touches the parabola → discriminant = 0
✔️ Condition for Tangency
Deriving tangent condition using:
• Discriminant method
• Parametric point method
• Slope method
How to check if a given line is tangent
Tangent & Normal to Parabola
Tangent at point and its slope formula
Geometric meaning of the normal line
parametric coordinates (at^2,2at)
Tangent in parametric form
Normal in parametric form​
describe chords, tangents, and normals
Important Parabola Theorems Covered
Tangent at point subtends a right angle (90°) at the focus
Tangents at endpoints of any focal chord:
• meet on the directrix
• are orthogonal (perpendicular)
Harmonic Mean Theorem:
The harmonic mean of segments of a focal chord = semi-latus rectum

Each theorem is proved with diagrams, logic, and exam-friendly reasoning.

🎯 Best For

✔️ Class 12 Mathematics – FBISE
✔️ National Book Foundation (NBF) new syllabus 2025
✔️ ICS / Pre-Engineering Students
✔️ Entry Test Preparation – NET • ECAT • FAST • GIKI • PIEAS • LUMS SSE
✔️ Students aiming for strong geometric intuition in conics
✔️ Board exams + MCQs + university level foundations

💡 Why Watch This Video?

This lecture turns complicated tangent–normal algebra into clear, intuitive geometry.
You will understand:

why tangency condition works
why normals behave strangely
why focal chords have special relations
how parabola geometry links with focus and directrix
Perfect for competitive exams, board preparation, and conceptual clarity.

💡 Why Subscribe to Dr Rizwan Channel?

📘 PhD Scholar with 10+ years of teaching experience
🧠 Logical & visual explanations
🎥 Diagrams, animations & parametric visualization
📊 Board + Entry Test aligned lectures
🎯 SLO-based content
📚 Full coverage of Class 11 & 12 New Syllabus

🔍 Related Searches

Class 12 Math Exercise 7.5
NBF Exercise 7.5 Tangent & Normal
Conic Sections Advanced Parabola
Parametric Form of Parabola
Intersection of Line & Parabola
Focal Chord Condition
Tangent Normal Theorem
Class 12 Analytical Geometry
NBF 2025 Parabola Concepts
Board Exam Shortcuts Parabola

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