Parabola Tips

Assalam O Alaikum !
                                  As we know, chapter 6 (Conic Sections) of 2nd year is heart of math portion. So, you have to learn this chapter very seriously and carefully. I am sharing some simple tips about parabola which will surely help you a lot.
First of all, what is parabola?

Parabola : The parabola is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus

PARABOLA TIPS

• 1st Tip :
  For Example → Find the focus and vertex of x^2=-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 x^2).If we have equation like this y^2=-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(x^2=4y,x^2=-4y,y^2=4x,y^2=-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 y^2=8x(here a=2 and y=0) So x+8=0 is the directrix of this equation y^2=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 X^2=-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(X^2=-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 X^2=-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.