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shivam_bhalla
 2 years ago
For Points P=(x_1,y_1) and Q(x_2,y_2) of the coordinate plane a new distance d(P,Q) is defined by d(P,Q) = x_1  x_2+y_1y_2 Let O = (0,0) and A = (3,2). Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray . Sketch this set in a labelled diagram. (10 marks)
shivam_bhalla
 2 years ago
For Points P=(x_1,y_1) and Q(x_2,y_2) of the coordinate plane a new distance d(P,Q) is defined by d(P,Q) = x_1  x_2+y_1y_2 Let O = (0,0) and A = (3,2). Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray . Sketch this set in a labelled diagram. (10 marks)

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Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1The hardest part of this question is the language :/

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.2using the new distance definition, then for some point (x,y) setting the distance equal to both O and A \[\rightarrow x +y = x3 +y2\] now to show that is a union of line segment and ray ...

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.2hmm not a fan of absolute value functions

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1x + y = x3 + y2 Since it's the first quadrant, x and y shall be positive. x + y = x3 + y2 Now up till (2,2) The line should be x+y = x + 3  y + 2 2x + 2y = 5

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0yes. It is right. But I am facing the problem in understanding this question.

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0@Ishaan94 and @dumbcow , how would you proceed further??

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm they (the question) have defined a new distance formula.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1335436017723:dwAnd we are supposed to get the points which are equidistant from the points O and A, using the new distance formula. Is that right? @dumbcow

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0It should be the ditsnace individually. Suppose. See the dig belowdw:1335436193825:dw Like distance between O and P (by new distance formula) should be equal to distance between A and Q (by new distance formula)

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1I can't get the line after (3,2) x + y = x3 + y2 Hmm are you sure the equation is correct? @shivam_bhalla

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0It is a question from IITJEE .

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.2it seems that no points outside (3,2) are equidistant to O and A

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm but the result can't lie. Maybe you could check the equation again? because the question says an infinite ray and finite distance, and we didn't get the infinite one.

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0The question is correct. I have referred from 2 books. It is a math question from IITJEE year 2000 (main)

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0See here. Question 4 >http://www.askiitians.com/iitpapers/IITJEE2000mathematicsmains.aspx

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1Strange the question is right http://www.askiitians.com/iitpapers/IITJEE2000mathematicsmains.aspx

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1I have the 30 years, I will be back in a moment.

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.2http://www.wolframalpha.com/input/?i=abs%28x%29%2Babs%28y%29+%3D+abs%28x3%29%2Babs%28y2%29 looks like we forgot the case where y>2 but x<3 > x = 1/2

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1:/ and I was trying to blame the question

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0wish I have wolfram alpha with me in my exams. Thanks @Ishaan94 and @dumbcow for the help. I wish had 2 medals to give away

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.1lol, with enough practice you won't need wolfram. goodluck. :)

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0Study the 9 regions defined by the lines in the attacehd file, each one separtely. It would be easy to get rid the absloute sign. For eaxmple the bounded region we have \[ 0\le x \le 3\\ 0\le y \le 2 \] In this region we 3  x + 2 y = x + y 2 x + 2y = 5 y= x + 5/2 Study the othe regions and see what you can get.

shivam_bhalla
 2 years ago
Best ResponseYou've already chosen the best response.0@eliassaab , Thanks for your help. I had initially problem in understanding the question. But I am comfortable with modulus function, just that my brain had gone blank at that time after reading the question :)
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