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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Paragraph Consider A B C whose vertices are A (m, n), B (1,2), C (2,3) and vertex 'A' lies on the line 2 x-y+3=0 where m, n N with m^2+n^2=90 . Let area of A B C be S such that [S]=2 , where [x] denotes greatest integer less than or equal to x . Question: If the equation of side A C of A B C is a x+b y=9 , then (a+b) equals

Options

  1. A4
  2. B15
  3. C5
  4. D11

Correct answer

C. 5

Step-by-step solution

aligned & As A(m, n) lies on y=2 x+3 & n=2 m+3 & A=(m, 2 m+3) aligned Area of ABC = 1 2 | array ccc m & 2 ~m +3 & 1 1 & 2 & 1 2 & 3 & 1 array |= 1 2 | ~m +2|= S (Given) aligned & But [ S ]=2 2 S 3 & i.e., 2 1 2 | ~m +2| 3 aligned 4 |m+2| 6 Now, | m +2| 6 -6 m +2 6 -8 m 4 (1) and |m+2| 4 m+2 4 or m+2 -4 m 2 or m -6 From (i) and (ii), we get -8 m -6 or 2 m 4 m =-7,-6,2,3 But m N , So, m -7,-6 aligned & m=2,3 & Also m=2 n=2 m+3=2(2)+3=7 & A(2,7) aligned aligned & But m ^2+ n ^2=90 and 2^2+7^2 90 & ~m 2 & Now m =3 n =2

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