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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Paragraph: aligned & Let f(a, b)= 49+a^2-7 2 a + b^2+50-10 b + a^2+b^2- 2 a b (a, b R⁺ ) & g(a, b)= a^2+b^2 + a^2+b^2-2 a+1 + a^2+b^2-2 a+1 + a^2+b^2-6 a-8 b+25 & (a, b R) and h(a)= | a^2+4 a+5 - a^2+2 a+5 |(a R) aligned Question: Least value of (a, b) :

Options

  1. Ais equal to 12
  2. Bis equal to 13
  3. Cis equal to 15
  4. Ddoes not exist

Correct answer

A. is equal to 12

Step-by-step solution

aligned & f(a, b)= a^2 2 + a^2 2 -7 2 a+49 + (b-5)^2+5^2 + a^2 2 + a^2 2 +b^2- 2 a b c & f(a, b)= ( a 2 )^2+ ( a 2 -7 )^2 _ P Q + (b-5)^2+5^2 _ R S + ( a 2 )^2+ ( a 2 -b )^2 _ R Q & aligned Image of R is R^ in y=x Q R=Q R^ Also S R=S R^ and image of S is S^ aligned & R^ S=R^ S^ & P Q+Q R^ +R^ S^ P S^ & S R=S R^ =S^ R^ aligned Sum of 3 sides of quad. >4 th side Min. value if P S^ = 144+25 = 169 =13

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