Math Sat Ii C Tough Questions

Test Preparation
1

<li>The Graph of (x-2)^2 = 4y has a
a) vertex at (4,2)
b) focus at (2,0)
c) directrix at y = -1
d) latus rectum 2 units in length
e) none of these</li>
</ol>

<p>answer is C…Problem is I dont know how to figure out any of these things</p>

<li>Which of the following is an asymptote of 3x^2 - 4y^2 -12 = 0?
a) y = 4/3x
b) y = -2/rad(3)
c) y = -3/4x
d) y = rad(3)/2x
e) y = 2rad(3)/3x</li>
</ol>

<p>Answer is D… No clue how to figure this out</p>

<li><p>The area bounded by the curve y = rad(4-x^2) and the x-axis is
a) 4pi
b) 8pi
c)16pi
d)2pi
e)pi
Answer is D… Anyone can do this one?</p></li>
<li><p>Which of the following is theequation of the circle with center at the origin and tangent to the line with equation 3x - 7y = 29?
a) x^2 + y^2 = 12
b) 2x^2 + 2y^2 = 29
c) x^2 + y^2 = 15
d) 3x^2 + 3y^2 = 40
e) x^2 + y^2 = 10</p></li>
</ol>

<p>Answer is B… no idea on this one either</p>

<li>An equilateral triangle is inscribed in the circle whose equation is x^2 + 2x + y^2 - 4y = 0. THe length of the side of the triangle is
a) 5
b) 1.9
c) 2.2
d) 3.9
e) 4.5
Answer is d… anyone explain this one?</li>
</ol>

<p>If you guys can explain any of these itd be helpful thaanx…</p>

2

<ol>
<li><p>If you don't know the definitions for these terms, do a Google search. There are plenty of good references out there, which also show how to compute them.</p></li>
<li><p>Asymptotic behavior should describe the behavior of the function at very large values of x. Typically, the effect of constants like the '-12' practically vanishes here; the curve would behave vey much like</p></li>
</ol>

<p>3x^2 - 4y^2 = 0
or 4y^2 = 3x^2
2y = x sqrt(3)
y = (sqrt(3)/2) x</p>

<ol>
<li>This is just the equation for a circle, written in non-standard form.
If y = rad(4-x^2), then
y^2 = 4 - x^2
x^2 + y^2 = 4 = 2^2, which is a circle centered at (0,0) with radius=2 .</li>
</ol>

<p>What's its area? And since half its area lies above the x-axis, what's (0.5) area?</p>