17 equations that changed the world.

Pythagoras Theorem

Pythagoras Theorem :- A theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

h² = P² + B²

Infinite Series : - Convergence and Divergence, Alternating Series, Liebnitz's test, Absolute Convergence and Conditional Convergence

Integration formula

Formula of Conic Section

1. Formula of circle

(x-h)² + (y-k)² = r²
Where C(h,k) is centre
P(x,y) is point on circle
And CP = r is radius of circle




2. Formula of parabola
       

 Directrix is called the fixed line.
Focus is the fixed point F.
Axis of parabola is a line through the focus and perpendicular to the directrix.

 

*  y² = 4ax

 * y² = -4ax

 

* x² = 4ay

* x² = -4ay







Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola.

Length of latus rectum = 4a

Question 16, Chapter 7, Class 12, Mathematics, NCRT ,CBSE

Solution 16.

A TEXT BOOK of MACHINE DESIGN by R.S Khurmi and J.K Gupta