Mathematics
Coordinate-Geometry
Easy

Question

text  A point on the straight line,  end text 3 x plus 5 y equals 15 space text  which is equidistant from the coordinate axes will lie only in -  end text

  1. 1 to the power of text st  end text end exponent comma 2 to the power of text nd  end text end exponent text  and  end text 4 to the power of text th  end text end exponent text  quadrants  end text
  2. 1 to the power of text st  end text end exponent text  and  end text 2 to the power of text nd  end text end exponent text  quadrants  end text
  3. 4 to the power of text th  end text end exponent text  quadrants  end text
  4. 1 to the power of text st  end text end exponent text  quadrants  end text

The correct answer is: 1 to the power of text st  end text end exponent text  and  end text 2 to the power of text nd  end text end exponent text  quadrants  end text

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I n space a space n o n minus r i g h t minus a n g l e d space t r i a n g l e space increment P Q R comma space l e t space p comma space q comma space r space d e n o t e space t h e space l e n g h t s space o f space t h e space s i d e s space o p p o s i t e space t o space t h e space a n g l e s space a t space P comma space Q comma space R space r e s p e c t i v e l y. space T h e space m e d i a n space f r o m space R space m e e t s space t h e space s i d e space P Q space a t space S comma space t h e space p e r p e n d i c u l a r space f r o m space P space m e e t s space t h e space s i d e space Q R space a t space E space a n d space R S space a n d space P E space i n t e r s e c t space a t space O. space I f space p equals square root of 3 comma space q equals 1 comma space n d space t h e space r a d i u s space o f space t h e space c i r c u m c i r c l e space o f space t h e space increment P Q R space e q u a l s space 1 comma space t h e n space w h i c h space o f space t h e space f o l l o w i n g space o p t i o n s space i s divided by a r e space c o r r e c t space ?

I n space a space n o n minus r i g h t minus a n g l e d space t r i a n g l e space increment P Q R comma space l e t space p comma space q comma space r space d e n o t e space t h e space l e n g h t s space o f space t h e space s i d e s space o p p o s i t e space t o space t h e space a n g l e s space a t space P comma space Q comma space R space r e s p e c t i v e l y. space T h e space m e d i a n space f r o m space R space m e e t s space t h e space s i d e space P Q space a t space S comma space t h e space p e r p e n d i c u l a r space f r o m space P space m e e t s space t h e space s i d e space Q R space a t space E space a n d space R S space a n d space P E space i n t e r s e c t space a t space O. space I f space p equals square root of 3 comma space q equals 1 comma space n d space t h e space r a d i u s space o f space t h e space c i r c u m c i r c l e space o f space t h e space increment P Q R space e q u a l s space 1 comma space t h e n space w h i c h space o f space t h e space f o l l o w i n g space o p t i o n s space i s divided by a r e space c o r r e c t space ?

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text  A rectangle is inscribed in a circle with a diameter lying along the line   end text 3 y equals x plus 7. text  If the two adjacent vertices   of the  end text
text rectangle are  end text left parenthesis negative 8 comma 5 right parenthesis text  and  end text left parenthesis 6 comma 5 right parenthesis comma text  then the area of the rectangle (in sq. units) is :  end text space

text  A rectangle is inscribed in a circle with a diameter lying along the line   end text 3 y equals x plus 7. text  If the two adjacent vertices   of the  end text
text rectangle are  end text left parenthesis negative 8 comma 5 right parenthesis text  and  end text left parenthesis 6 comma 5 right parenthesis comma text  then the area of the rectangle (in sq. units) is :  end text space

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