[Music] do you know what's the shape of a dish satellite called that's right a Dish satellite is parabolic in shape we've seen this in one of our previous videos it's made up of this type of a curve we can find many such examples of parabolic surfaces in our daily lives one of them is the mirror used in a flashlight it's also made up of this type of a curve let's consider just one of all these curves such a curve is called parabola in this video we will understand what exactly a parabola is we can see that a parabola looks like a u-shaped curve but every u-shaped curve is not a parabola a parabolic curve has a specific property that makes it a parabola let's begin with understanding why the dish satellite or the mirror in the torch is parabolic in shape in the case of the dish satellite due to the parabolic shape all the incoming signals falling on the dish are reflected towards a single point this is where the receiver is placed so the parabolic shape helps in concentrating all the incoming signals at a single point such a point for parabola is called its focus and every parabola has a focus point and this is what makes a parabola so useful for example in the case of a torch a bulb is placed at the focus of the parabolic mirror we know the light emitted by the bulb spreads in all directions but due to the parabolic mirror the light emitted in this direction is reflected in the forward direction like this so we see that a parabola is a u-shaped curve related to which there is a special point called its focus a focus point of a parabola is similar to the center point of a circle and so in the case of a circle a parabola is actually defined using its focus point let us see how let's take a point in a plane and name it as point F also let's take a straight line and name it L now please listen carefully to what I'm going to say next we will now consider points which are at an equal distance from point F and a line L are there any such points on this plane yes consider this point P one it will be at an equal distance from the point F and the line L consider another such point P - its distance from point F will also be equal to its distance from the line L another obvious point is the midpoint of the perpendicular segment connecting point F to the line L all such points that satisfy this condition will lie on this curve and such a curve is called a parabola so how can we define a parabola we see that a parabola is the set of all points in a plane that are equidistant from a fixed point F and a fixed line L their given special names the point F is called the focus of the parabola and line L is called its directrix notice that the shape and the position of the parabola will depend on the position of point F and line L that is depending on the point we take as our focus and a line which we take as the directrix we will get different parabolas let's say for example we increase the distance between the focus and the directrix here so let's take this point as the focus and this line as the directrix corresponding to this focus and this directrix this will be our parabola now say we take this horizontal line as our directrix and this point as our focus so what will the parabola look like here this will be the parabola here so we see that depending on the focus and the directrix we get different parabolas now consider one last thing in this parabola let's draw a line that's passing through the focus and is perpendicular to the directrix notice that the part of the parabola above the line is the mirror image of its spot below this line that is the parabola is symmetric about this line this line for a parabola is called as its axis and the point where the parabola intersects the axis is called its vertex note that the distance of the vertex from the directrix is the same as its distance from the focus okay now can you tell me what will be the access and the vertex of these two parabolas for this parabola this line will be its axis and this point will be its vertex similarly for this parabola this will be its axis and this will be its vertex so in this video we saw what a parabola is it's a collection of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called directrix in the next video we will find the equation of a parabola to stay updated please subscribe to our Channel [Music] you