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Parabola,
SHORTCUT,
TIPS & TRICKS
HYPERBOLA,PARABOLA and ELLIPSE TIPS
Here you find all types of ticks regarding to
Parabola,Hyperbola And Ellipse Chapter.This chapter like the heart of Math Portion because 2-3 question ask from this chapter.So,Friends you have to learn this chapter more carefully and more successfully.
I am going to share you a simple tricks which I remembered and it helped me a lot.So let's start.
PARABOLA TIPS
→ 1st Tip
| For Example → Find the focus and vertex of x2=-24y??? |
| Focus → First of all see in the question where is the square whether it is in x or y.After seeing the square,think (0,a)(where 0 is replaced because x2).If we have equation like this y2=-24x then we think (a,0) because here y is squared.So now we have to find a?.a is simple to find co-efficient of degree 1 is equal to 4a(-24=4a).After solving this we get a=-6.So the focus of this equation is (0,-6). |
| Vertex → Vertex of all these types of equation(x2=4y,x2=-4y,y2=4x,y2=-4x) is (0,0) |
| Directrix → Directrix is directly related to a and sign of squared value.See above example where x is squared so mean x=0(reference read focus portion) and a=-6(reference read focus portion).So we get directrix y-6=0.If we have an equation like this y2=8x(here a=2 and y=0) So x+8=0 is the directrix of this equation y2=8x |
Sometimes questions asked like this → Find the equation,if focus(0,-8) ,vertex(0,0) and options are given.
| Simply you have to find focus of given options if any one of the option is matched with given focus,then that will be the correct answer of given condition. |
→ 2nd Tip
| For Example → Find the focus and vertex of (x-1)2=-24(y-2)??? |
| First of all suppose x-1=X and y-2=Y.So the equation becomes X2=-24Y |
| Focus → =Find Focus of this equation is same as that of above i.e:(0,-6).But here you have to follow one more step as seen from this focus X=0 and Y=-6 So you have to put value of X i.e.x-1 and Y=y-2.So,we get x-1=0 and y-2=-6,by solving this we get x=1 and y=-4 so Focus becomes(1,-4). |
| Vertex → Vertex of this equation(X2=-24Y) is (0,0).Then,you have to follow same rule as that of focus.X=0 and Y=0 .Putting the value of X and Y.we get x-1=0 and y-2=0.By solving this we get x=1 and y=2.So the vertex of this equation becomes (1,2) |
| Directrix → .Here we apply same rule as that of Example-1.We have equation X2=-24Y.So here Directrix is equal to Y-6.Putting the value of Y |
Sometimes questions asked like this → Find the equation,if focus(0,-8) ,vertex(0,0) and options are given.
| Simply you have to find focus of given options if any one of the option is matched with given focus,then that will be the correct answer of given condition. |
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