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JEE Main202522 Jan 2025Morning ShiftMathematicsParabolaActual

Let the parabola y=x^2+ p x-3 , meet the coordinate axes at the points P , Q and R . If the circle C with centre at (-1,-1) passes through the points P, Q and R , then the area of P Q R is :

Options

  1. A7
  2. B4
  3. C6
  4. D5

Correct answer

C. 6

Step-by-step solution

y = x ^2+ px -3 Let P ( , 0), Q ( , 0), R (0,-3) Circle with centre (-1,-1) is (x+1)^2+(y+1)^2=r^2 Passes through (0,-3) aligned & .1^2+(-2)^2=r^2 ] & r ^2=5 aligned (x+1)^2+(y+1)^2=5 Put y =0 aligned & (x+1)^2=5-1 & (x+1)^2=4 & x+1= 2 & x=1 or x=-3 & P(1,0) and Q(-3,0) aligned Area of PQR = 1 2 | array ccc 1 & 0 & 1 -3 & 0 & 1 0 & -3 & 1 array |=6

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