P is a point on the parabola y^2=4 x where abscissa and ordinate are equal. Equation of a circle passing through the focus and touching the parabola at P is:

Step-by-step solution

a t^2=2 a t point t =0, t =2,(0,0), (4,4) (I) when P (0,0) x ^2+ y ^2+ ( x )=0 pass the (1,0) =-1 , equation tagent al (0,0) y ^2=4 x Equ. x^2+y^2-x=0 aligned & y y₁=2 (x+x₁ ) & x=0 aligned (II) when point (4,4), 2 x-2 y+8=0(x-4)^2+(y-4)^2+ (2 x-2 y+8)=0 pass (1,0) Equation x^2+y^2-13 x+2 y+12=0