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AP EAMCET201920 Apr 2019Morning ShiftMathematicsParabolaActual

The parabola (x^2=4 ) ay makes an intercept of length ( 40 ) units on the line (y=1+2 x ), then a value of (4 a ) is

Options

  1. A2
  2. B-2
  3. C-1
  4. D4

Correct answer

B. -2

Step-by-step solution

Since length of the chord intercepted from the line (y=m x+c ) by the parabola (x^2=4 a y ) is (4 a (1+m^2 ) (c+a m^2 ) ) So, ( 40 =4 a( l +4)( l +a(4)) ) ( array lc & 40=16(5 a(1+4 a)) & 1=2 a(1+4 a) & 8 a^2+2 a-1=0 & 8 a^2+4 a-2 a-1=0 & 4 a(2 a+1)-1(2 a+1)=0 & a= 1 4 or - 1 2 & 4 a=1 or -2 array ) Hence, option (2) is correct.

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