<p>hi everyone. i bet no one can solve this. i was doing my math test yeasterday and no one in my class could solve it. But it has just stucked in my mind and has become a fixation if i don’t solve it. the problem is:
u have a parabola with equation x^2=4pY (p>0). also u have a circle whith equation X^2+Y^2=R^2 and the diameter of the circle is 3p. Now u have to proov that the comon cord of the circle and the parabola bisects seg OF. where O is the center of the circle and of the parabola and F is the… (damn it i am albanian and i dont know english terms but the coordinate of F is (b/4;0) i think you know what F is now).</p>
<p>I think this question was there in the last few pages of my textbook- the conics chapter. My exams are over so I cant be buggered…sorry.</p>
<p>P.S. Draw the diagram, and take parametric coordinates.</p>
<p>Focus dude, FOCUS </p>
<p>:D ;)</p>
<p>if anyones got the balls , then solve this - </p>
<p>sinx/n = ???</p>
<p>no other data given.</p>
<p>lets see whose got brains now.</p>
<p>(if you know it from before then dont spoil the fun)</p>
<p>SIX? haha.</p>
<p>and btw olsi, what was the qn? i read thru your thread, but cant seem to find the qn!</p>
<p>“if anyones got the balls , then solve this”
You dont need balls to solve it.</p>
<p>are you sure about “F is (b/4,0)” ? and what is b?</p>
<p>why not do secx/c ?</p>
<p>@ yryuan b=4p (in this case, usually b is the koeficent before y). and yeah i am sure that that’s the coordinate of F (4p/4, ) or (p,0)… uuuu… i think i got the question wait a minute…</p>
<p>hey i found it. as i told u the coordinates of F are (p;0). Also 0 is (0;0). so the distance betwen 0F is p and it is found on the y axis (because center of circle (0;0) and center of parabola (0;0). So the task is to proof that the coordinate of the intersection of the common cord and OF are A (0:0.5p). now u just have to for a system of equations </p>
<p>x^2=4pY
X^2+Y^2=2.25p^2 (diameter = 3p r=1.5p)</p>
<p>X^2=R^2-Y^2
x^2=4pY</p>
<p>2.25p^2-Y^2=4py</p>
<p>Y^2+4py-2.25p^2=0</p>
<p>a=1 b=4p c=-2.25p^2</p>
<p>D=16p^2+9p^2=25
-4p+(-)5p y1=-9p (not allowed because p>0 so y>0
1Y2=-------------
2 YA=0.5P (ALLOWED)
fin x which s X^2=4p(0.5p) =2p^2 so X=+(-)1.4p</p>
<pre><code> X1+X2 1.4p-1.4p 0
</code></pre>
<p>NOW XA=--------=-----------=-----=0 Bingo
2 2 2</p>
<p>so i prooeved that the coordiantes of the intersection are (0:0.5p) and which is the center of OF. WOOOW i managed to solve it. thank you menss</p>
<p>hey now that is poted the message it didnt show up as i wrote it, but i think u can manage to understand it though.</p>
<p>@ scandal-less Sinx/n=??? can u please help us. What r we suposed to do to find a definite value or just transform it whith identical transformation.</p>
<p>olsi from your solution it seems F should be(0,p). (p,0) would be on x-axis. btw it’s such an easy question (don’t mean anything else) :D</p>
<p>yeah,ur right yryuan23. i rushed… but the right coordinates (at the begining of my solution) are F (0;b/4). So i had to proof that the coordintes of the intersection are (0;p) and lies on the y axis (u should have figured out it urselfe considering that this was SUCH AN EASY QUESTION TO YOU.</p>
<p>six is right !</p>
<p>your a smarty :p</p>
<p>rishabh, how is it six?</p>
<p>cancel ‘n’ in the numerator and denominator</p>
<p>simple</p>
<p>should i laugh now?! hahaha. one of the least funiest things i’ve ever read. nevertheless, a quiz for you:</p>
<p>5 hats. 3 of which are red and 2 are white.
3 sailors in a row. The last sailor can see what hats do the infront of him sailors have on. The middle one can watch the in front of him sailor hat but not the one behind him. The first sailor cannot see any of the hats. Now, the captain of the ship assigns one at hat randomly to each sailor. After the distribution has been made, the last sail says whith loud voice: " by watching the colour of the 2 hats each of my friends has i cannot determine what colour is my had". The second sailor said" by watching the colour of the infrontof me sailore AND BY HEARING MY BEHIND FRIEND COMMENT I CANNOT dettermine the color of my hat". The first sailor than said " then the colour of my hat is…"</p>
<p>If anyone finds it out(and a breif explanation is needed because a blinded guess would give u 50% possibility) post the answer here and f possible the SAT I math score</p>
<p>twasn meant to be funny. twas meant to be stoopid. intelligent people cant answer stoopid questions.</p>
<p>Red.</p>
<p>Last sailor can only determine his color if the front two have both white hats. But he can’t, so the front two can have either both red, or one red and one white. If the first sailor has white, then the middle sailor must have red, otherwise the last sailor is lying. But if the front sailor has red, then the middle sailor can have either red or white hat. Since middle sailor says he can’t determine, it means front sailor has red hat.</p>
<p>Nice question, but easy. Here is another -</p>
<p>Three ants sit in a row (not a circle). Front one says, I have two ants behind me. Back one says I have two ants in front of me. The middle one says I have two ants in front and two ants behind me. How so? :p</p>
<p>they should be in a circle but you say theyre in a row eh ?</p>