[Music] hello mahamat in this video lesson we will discuss the introduction of hyperbola standard form of the equation of hyperbola so up against standard equation is standard equation at n i x squared over a squared minus y squared over v squared is equal to one is x squared over a squared e being sub n transverse axis nothing i horizontal origin and then kappa young equation not then y squared over a squared minus x squared over b squared is equal to one in transverse axis not in a vertical and ganon paden a y squared over a squared vertical in the manual transfers axis net n and then capacity equation at n the quantity of x minus h squared over a squared minus the quantity of y minus k squared over b squared is equal to one in transverse axis nothing is horizontal so equation at n y minus k squared over a squared minus the quantity of x minus h squared over b squared is equal to one so i'm known and that indeed y minus k squared over a squared vertically and transverse axis not n so saying now i'm centering [Music] origin [Music] is determined by a constant and two fixed point it's called the focus point hyperbola transverse axis however instead of the sum of the two distance as being a constant as with an ellipse in the case of hyperbola the difference between two distances is constant more specifically the hyperbola determined by a pair of fosi and again a given constant is the set of points x y in the plane such that the absolute value of the difference between the distances from x y to the force i is equal to the constant parts of the hyperbolas the parabola has two branches the two branches can open either right or left or up and down so [Music] capacity engine transverse axis net engine horizontal eb7 horizontal transverse axis and then your vertex known parabola depending on whether the fosi are the horizontal or vertical axis so each branch of the hyperbola has a vertex and the center of the hyperbola is the midpoint of the line segment joining the vertices [Music] [Music] and then foreign for example uh an equation at the end x squared over a squared minus y squared over b squared is equal to one so under being orientation and hyperbola 10 so in x squared over a squared minus y squared over b squared is equal to one malware nothing in vertex [Music] us is equal to the square root of a squared plus b squared so it is net in so making a tower time conjugate axis so your conjugate axis not an i uh perpendicular shadow horizontal axis nothing constantly vertex and then your fossil okay past in cnn focus so nothing more infosight since now by getting the value of c ma nothing you focus champlain the distance between the uh the distance from the center to vertex senior volume and a backup kappa y squared over a squared minus x squared over b squared is equal to one i'm getting equation at n at my net you've known this equation not in a y squared over a squared a b sub n vertical okay so vertical the magnet transfers access net n and then solid at the market vertices net n and then you focus nothing not n that is negative though so in b sub 1 at the bottom start times the left side so negative b zero and then b sub to that and b zero so parama zero negative c same with the lattice rectum using the formula b squared over a so tatan that nothing class uh you a not indito i betting may be shorter or longer the transverse axis so marine wallet in conjugate axis i must mahaba [Music] the fundamental rectangle of the hyperbola that is the graph of x squared over a squared minus y squared over b squared is equal to one so parasan so no connect vertices vertex not n vertex one vertex 2 vertex nothing let's go vertex number 2 rectangle hyperbola class melatonin asymptotes so the asymptotes of this hyperbola contain the diagonals of the rectangle and half equations so by the gamma equation at all y is equal to b over x and y is equal to negative b over a x so happening equation you my negative in sign paganito yang okay and in diagonal nothing eternal positive so it dt thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button but updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel