Tangents and Normals pdf notes


 A tangent to a curve is a line that touches the curve at one point and has the same slope as the curve at that point. ... A normal to a curve is a line perpendicular to a tangent to the curve.


Let's learn more about it,


Tangents and Normal


Prefer it and enjoy Mathematics.


Sorry for any Mistake.


Share it to all.


Comments

Post a Comment

Popular posts from this blog

If you are wearing these clothes then your rites are wrong!

  "If You Are Wearing These Clothes, Then Your Rites Are Wrong!" — A Misguided Judgment In today’s world, we often hear harsh and unfair statements like this. “If you're wearing ripped jeans, you're disrespecting your culture.” “If you wear traditional clothes, you’re outdated.” “If you don’t dress ‘properly,’ you’re not raised well.” But let’s stop and ask ourselves: Since when did clothes start defining our character, values, or the way we were raised? The Misconception Too often, people judge others based solely on what they wear. A person wearing modern, Western-style clothing might be seen as “spoiled” or “rebellious.” Meanwhile, someone in traditional attire is labeled as “conservative” or “boring.” But the truth is: Clothing is a personal choice. Culture and values come from the heart, not from the fabric you wear. Your rites — your beliefs, your values, your manners — are shaped by how you treat others, how you speak, how you act in tough situations,...
Read more

Self Sacrifices

Image
The Meaning and Power of Self-Sacrifice When we learn something, the most important question we should ask is why we are learning it. Understanding the reason behind a concept gives it true value. One such concept is self-sacrifice . A self-sacrificing person is someone who gives up what they want so that others can have what they need or desire. For example: “These people were unselfish, self-sacrificing, and sincerely concerned about the general good. His courage and self-sacrificing devotion to duty resulted in the loss of his life.” Sacrifice is not just about giving things up — it is a path to help others. But here's an important point: if you truly make a self-sacrifice, never go around telling others about it. Real sacrifice is silent. If it is done with a pure heart, it brings a unique kind of joy that doesn’t need recognition. Many people think that if they tell someone about their sacrifices, that person will change or become more grateful. Unfortunately, that's ...
Read more

What will you do... (Part 1)

Image
  What will you do when you or your parents are called corrupt? Don’t Judge Without Knowing — A Personal Lesson in Understanding When I was a teenager, I faced a moment that left a lasting impression on me. One day, I heard that a friend of mine had called my father corrupt . I was shocked and hurt. Out of anger, I argued with him, and the fight turned into a serious quarrel. Eventually, the incident was reported to our class teacher — and he informed my father. I expected my father to be upset or angry. But instead, he calmly said something I will never forget: "Even if someone calls me corrupt, I don’t become corrupt. What matters is that you know who I am, and I know who I am." Those words opened my eyes. My father was right. No matter what others say, our character isn't defined by someone else's opinion . What truly matters is who we are on the inside, not the labels others try to place on us. A Message to Remember People often judge others too quickly. Somet...
Read more