Let the shortest distance from ( a , 0), a 0 , to the parabola y^2=4 x be 4 . Then the equation of the circle passing through the point (a, 0) and the focus of the parabola, and having its centre on the axis of the parabola is :

Step-by-step solution

Normal at P aligned & y+ t x=2 t+t^3 & &( a , 0) & at = 2 t + t ^3 & a = 2+ t ^2 & R (2+ t ^2, 0 ) aligned aligned & PR =4 4+4 t ^2=16 & 4 t ^2=12 t ^2=3 & a =5 R (5,0) aligned Focus (1,0)(1,0) &(5,0) will be tha end pts. of diameter Eg ^ n of circle is aligned & (x-1)(x-5)+y^2=0 & x^2+y^2-6 x+5=0 aligned