hello everyone welcome to senior pablo tv so after discussing our circle let's now proceed in our second kind of chronic section the parabola before watching this video please make sure that you subscribe in our channel and click our notification bell in order for you to be updated in our upcoming videos the parabola first let us define the parabola is the locus of all points whose distance from a fixed point our f and a fixed line for the l not passing through through f are the same the fixed point is called the focus while the fixed line is called the directrix so when you were in grade nine you already discussed the parabola but in your grade 11 there are [Music] mathematical terms that you will encounter just like our focus and directrix later we will discuss that in our graph to better understand we know that parabola is a curve can be open upward sideward the left opens to the right or opens downward those are the graph of parabola note the line that passes through the focus and is perpendicular to the directrix is called the axis of symmetry of the parabola and the lattice rectum is the line that passes through a focus perpendicular to the axis of symmetry okay to better understand those mathematical terms let us locate it in our cartesian plane and our graph let's say this is our parabola okay this curve and this curve opens upward we have here the focus that is the fixed point so where is our focus here so this is our focus this is our focus okay where is the directrix while the fixed line is called the directrix so this is our directories a line fixed line not passing through the focus are the same this is our directrix next term is the axis of symmetry the line that passes through the focus and is perpendicular to the directrix a line passes through the focus this is our directrix that is perpendicular to our directrix so this is our axis of symmetry axis of symmetry and the lattice rectum is a line that passes through the focus perpendicular to the axis of symmetry so this line passes through the focus and it's perpendicular so this is the lattice rectangle lattice in parabola we're going to find the length of lattice rectum okay so that is the definition and different terms in our parabola now we're going to find the axis of symmetry directories focus and lattice rectum of the parabola using the given equation station and now let's have this example determine the opening vertex focus directrix axis of symmetry and endpoints of lattice rectum of the parabola with the given points then graph so we're going to find the opening opening opening whether it is upward downwards to the open to the left or open to the right then the vertex focus directrix axis of symmetry and endpoints of the lattice rectum given the parabola x squared is equal to 12 y okay let's have first the standard equation of parabola so that we can easily solve this problem so if our equation is at vertex point okay this is the vertex form of our of the equation of the parabola vertex form x squared is equal to 4cy and if this is the given x squared is equal to 4cy that means it opens upward because c is greater than zero and if it is in h k form so this will be the equation of the parabola and x squared is equal to negative four c y at vertex form take note c is less than zero that means open downward and this will be the equation for hk and opens to the right to the right if c is greater than zero then open to the left if c is less than zero so we have different formulas here that we are going to use for c is the length of the lattice rectum for c this one and c is the distance from the vertex to the focus from the vertex to the directrix so later on after graphing our problem you're going to understand this then 2c the distance from the vocals to the endpoints of the lattice rectum using this table we're going to find first the opening so x squared is equal to 12 y so that is in the so our vertex is zero zero so vertex we can look at that zero zero then we are in this form c is greater than zero or the p is greater than zero that means our opening is up more next find the focus directories and axis of symmetry so first let us find the focus to find the focus let us find first the value of c so to find the value of c we have here 4 c is equal to this is our 4c which is 12. for c oh we need to find c so we need to divide by 4. so c is equal to three twelve divided by four that is three that means from our vertex that is three units up to our vertex so our focus is zero positive three this is our focus now let's plot in our partition plane we know that our vertex is zero zero so let us locate zero zero in our origin with our focus we know that it's open upward so that means it is located up of our origin so zero three okay in the focus one two three this will be our points okay this is our focus focus is 0 3 and this is the vertex now let us find directrix so we have directories directrix is perpendicular to our axis of symmetry so that is three units below our vertex three units below so that is zero going down one two three negative three but directrix is a line so we're not going to plot the points we're going to find the equation so y is equal to negative 3 because directrix is a line okay y is equal to negative 3 so if we're going to find y is equal to negative 3 it's here is located here so just create a line passing it to negative three this will be our directrix next after getting the directrix we're going to find the axis of symmetry axis of symmetry axis of s let's say axis of x axis of x s or symmetry is perpendicular to the directrix so it's here passes through the focus so that is x our value of x that is zero so it's here along the okay now we're going to find the end points of the lattice rectum of the parabola so since we have c here and we have the formula of 2c the distance from the focus to the endpoints of the lattice rectum so 2c substitute so 2 times our c is 3. so from the focus to the end of the lattice rectum is six units so we're going to count six units to the left the left and to the right so one two three four five six and one two three four five six so our points are six and one two three three here we have negative six and positive three now connect our points from the endpoint of the lattice rectum going to our vertex then going to the another endpoint of the elastic that's on how to find the opening vertex focus directrix and the length of the lattice rectum or the endpoints of the lattice rectum now if your teacher asks you what is the length of the lattice rectum so the length of the lattice rectum is 4 times c that is 12. so length of lattice rectum is 12 units so that's it that's the problem now your turn i want you to answer this equation our assignment i'm going to write where is this [Music] the equation is y squared is equal to negative eight your assignment y squared is equal to negative 8 thank you for watching senior pablo tv our next lesson is what if the given is in the vertex h k or our vertex is h k in this form how we are going to find directrix axis of symmetry lattice rectum the focus and the vertex stay tuned for our next video