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Find the vertex, focus, directrix, latus rectum and axis of the parabola:(i) $y^{2}=18 x$(ii) $y^{2}=36 x$;(iii) $3 y^{2}=20 x$(iv) $x^{2}=7 y$;(v) $x^{2}=-8 y$,(vi...

Question

Find the vertex, focus, directrix, latus rectum and axis of the parabola:(i) $y^{2}=18 x$(ii) $y^{2}=36 x$;(iii) $3 y^{2}=20 x$(iv) $x^{2}=7 y$;(v) $x^{2}=-8 y$,(vi) $3 x^{2}=8 y$

Find the vertex, focus, directrix, latus rectum and axis of the parabola: (i) $y^{2}=18 x$ (ii) $y^{2}=36 x$; (iii) $3 y^{2}=20 x$ (iv) $x^{2}=7 y$; (v) $x^{2}=-8 y$, (vi) $3 x^{2}=8 y$



Answers

Find the vertex, focus, and directrix of the parabola and sketch its graph.

$ (x + 2)^2 = 8(y - 3) $

You have a parable equation? That is the quantity X ministries, verticals eight quantity Y plus one. So here we have the up board Our Abdullah The situation we've been general equation. The wanted text manage H squared goes toe for beating the quantity. Why mine escape that protects here We can't defined as h k for post 10 cities reference to the upward position. So we have each and KP that he supports most direct weeks. Yes. Why? Call list OK minus P. So here we have but given off h with this three. The hey here is negative. One for us is three. Then there is negative one personally determined. A p p here is or P is physicals toe keep Sophie is equals toe so base negative. Want us to that This focus at 31 there are direct tricks. Iss Why goals But negative one. That s k my nose too. So the direct tricks Sequels toe negative three. So here's how. Grab off parabola. It's for Osbourne Texan itself. It's direct tricks

Yeah, about a number 43. And of it, the question parable is given, which is why I, minus two whole square, equal to eight into X plus one X plus one. Let us compare this with our question. Why? Minus k Hold square, equal toe for a X minus one. This is for a for a X minus one. If you compare these two, we will be getting our vortex at gay as minus one and two. So this is the word X, Okay? No, it does draw the parabola. And one more thing we should calculate for equal to eat, so it must be equal to this. Will be used in during the parabola. So what? Texas minus one coming toe. Let us. Right. They said, Why exists? X axis. This is minus one. This is too. So this is the vertex minus one comma do. Okay, since yet there is a positive sign well designed with it. So parabola will be upward opening. Not a parts. Very. All right, we're opening. Okay, so let's just draw a line. Here. It is our excess of symmetry, and this is where takes this point. So our parable every look like this. Okay. An excess of symmetry is why equal to minus two who are sorry. Viable not Minister where Quito is our excess off symmetry. So this in minus one coming to Okay, No, we have valley of equal to two and is the distance off focus from Vertex. So if you move more two years right off minus two it will be one. It comes to zero and this will be one. So when comma to so it is very clear that focuses Focus is one comma one common toe So direct ICS will be two units left off this Vertex two years left off This vortex will be minus two and minus tree So directives will be X equal to minus tree The actress will be X equal to my instinct There is no need to do any gun collision. It is just graphical Thank you so

We have a problem Number 47 in which we have been given to parable one parabola Y plus three whole square, equal to eight into X minus two. Let us compare this ville. Why minus k all squared equal to for a X minus That so Vertex will be where text will be as in. Okay, that's common history. So it will be too and cable with my industry. So we have work takes to come on my industry, which is one of the answer. And again we can calculate for a equal toe eight, which means equal Toto, this will be this. This we will use letter. Okay, so let us draw that rough sketch of the parabola were Texas two comma minus three. Let's just Okay, this is too. This is minus three. So vortex will be here to common minus three litre vortex, which is here. And since here it is positive X was to eat so better when I will be opening the right wars. So a question of parabola and then Ah, graph of parabola. We look like this. So why call two? Minus three is the axis of symmetry. Let us change the color off this axis of symmetry. No distinct blooper. Excess off symmetry is liable to minus three. No easy call to two. And is the distance off focus from Vertex. And here focus will be obviously be at the right side of the verdict. So let us go. One unit, right toe the vortex. This is 212 years, right? This is three. This is four. And why, according will amend the same. So focus will be four comma my industry. So we have focused four comma, minus three. So this is one of the answers Vitter being asked. No direct tricks is the two units that is a unit left from the word X. So one unit is left from two is one and zero. So this itself is direct. X two y axis is the why is it that bad tactics? So it's a question will be X equal to zero. So this is the indirect tricks, and the graph is like this. Thank you so much.


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