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
- A2
- B-2
- C-1
- 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.