NUST-ENTRANCE-TEST-NET

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.

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PARABOLA TIPS

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For Example → Find the focus and vertex of x2=-24y???

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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).

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Vertex → Vertex of all these types of equation(x2=4y,x2=-4y,y2=4x,y2=-4x) is (0,0)

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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

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Sometimes questions asked like this → Find the equation,if focus(0,-8) ,vertex(0,0) and options are given.

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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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For Example → Find the focus and vertex of (x-1)2=-24(y-2)???

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First of all suppose x-1=X and y-2=Y.So the equation becomes X2=-24Y

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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).

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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)

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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

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Sometimes questions asked like this → Find the equation,if focus(0,-8) ,vertex(0,0) and options are given.

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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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Q # 1: How many terms of the G.S 1 + 4 + 16…. Must be taken to have their sum equal to 341. a) 4 b) 6 c) 5 d) 7 Answer Q # 2: If 3 + 3α + 3α2 + …….. = 25/8, then α = ? a) 6/11 b) 2/13 c) 7/15 d) None Answer Q # 3: Find 20th term of the series log 2 + log 4 + log 8 + log 16 + …….. a) 21log2 b) 20log2 c) log2 d) 10log2 Answer Q # 4 Find common fraction of 0.-45 a) 5/11 b) 5/13 c) 4/11 d) 3/11 Answer Q # 5: Geometric mean between 2√ 3and 6√ 3 is a) -6 b) ∓ 6 c) ∓ 5 d) None Answer Q # 6: What is the next number in the series 212, 179, 146, 113,… is ? a) 102 b) 96 c) 80 d) 84 Answer Q # 7: If 2, x, 32 are in G. P then x = ? a) ∓ 16 b) ∓ 8 c) ∓ 4 d) None Answer Q # 8: If the A.M between the roots of the quadratic equation is 8 and G.M is 5 then the equation is, a) x2 – 16x – 25 = 0 b) x2 + 16x – 25 = 0 c) x2 + 16x + 25 = 0 d) x2 – 16x + 25 = 0. Answer Q # 9 If 2x = 32 and 3y = 27 then xy = ? a) 5 b) 15 c) 10 d) 25 Answer Q # 10 The perimeter of an isosceles triangle is 36 cm, the altitude to the unequal side is 12 cm determine length of the sides a) 12,12 b) 14,8 c) 30,10 d) 13,10 Answer