Concept Builders - A Complete Guide To Entrance Test Examination: Conic Sections

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<span style="font-family: Times, Times New Roman, serif; font-size: large;">Assalam O Alaikum !</span><br />
<span style="font-family: Times, Times New Roman, serif; font-size: large;">                                  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.</span><br />
<span style="font-family: Times, Times New Roman, serif; font-size: large;">First of all, what is parabola?</span><br />
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<b><span style="color: #274e13;"><span style="font-size: large;">Parabola :</span> </span></b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.8400001525879px;">The </span><b style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.8400001525879px;">parabola</b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19.8400001525879px;"> is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus</span><br />
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<span style="box-sizing: border-box; font-weight: 700;"><span style="color: #660000; font-family: Times, Times New Roman, serif;">PARABOLA TIPS</span></span></div>
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<li style="box-sizing: border-box; text-align: left;"><span style="color: red; font-family: Times, Times New Roman, serif;"><b>1st Tip :</b></span><div style="box-sizing: border-box; font-size: 15px; line-height: 1.7em; margin-bottom: 20px;">
<em style="box-sizing: border-box;"><span style="font-family: Times, Times New Roman, serif;">For Example → Find the focus and vertex of x^2=-24y???</span></em></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="box-sizing: border-box; font-weight: 700;">Focus</span> → 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).</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="box-sizing: border-box; font-weight: 700;">Vertex</span> → Vertex of all these types of equation(x^2=4y,x^2=-4y,y^2=4x,y^2=-4x) is (0,0)</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="box-sizing: border-box; font-weight: 700;">Directrix</span> → 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</span></div>
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<span style="font-family: Times, Times New Roman, serif;">Sometimes questions asked like this → Find the equation,if focus(0,-8) ,vertex(0,0) and options are given.</span></div>
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<span style="font-family: Times, Times New Roman, serif;">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.</span></div>
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<li style="box-sizing: border-box; text-align: left;"><span style="color: red; font-family: Times, Times New Roman, serif;"><b>2nd Tip :</b></span><div style="box-sizing: border-box; font-size: 15px; line-height: 1.7em; margin-bottom: 20px;">
<em style="box-sizing: border-box;"><span style="font-family: Times, Times New Roman, serif;">For Example → Find the focus and vertex of (x-1)^2=-24(y-2)???</span></em></div>
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<span style="font-family: Times, Times New Roman, serif;">First of all suppose x-1=X and y-2=Y.So the equation becomes X^2=-24Y</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="box-sizing: border-box; font-weight: 700;">Focus</span> → =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).</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="box-sizing: border-box; font-weight: 700;">Vertex</span> → 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)</span></div>
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<span style="font-family: Times, Times New Roman, serif;"><span style="box-sizing: border-box; font-weight: 700;">Directrix</span> → .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</span></div>
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<span style="font-family: Times, Times New Roman, serif;">Sometimes questions asked like this → Find the equation,if focus(0,-8) ,vertex(0,0) and options are given.</span></div>
<div style="box-sizing: border-box; font-size: 15px; line-height: 1.7em; margin-bottom: 20px;">
<span style="font-family: Times, Times New Roman, serif;">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.</span></div>
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Parabola Tips

Assalam O Alaikum ! As we know, chapter 6 (Conic Sections) of 2nd year is heart of math portion. So, you...