Answer with Step-by-step explanation:
The equation of the parabola with focus (a,b) and directrix y=c is:
(x−a)²+b²−c²=2(b−c)y
Here, directrix is y= -2 i.e. c= -2
focus=(1,6) i.e. (a,b)=(1,6)
Equation of parabola will be:
(x−1)²+6²−2²=2(6+2)y
(x−1)²+36-4=2×8y
(x−1)²+32=16y
(x−1)²=16y-32
(x−1)²=16(y-2)
Hence, equation of parabola is:
(x−1)²=16(y-2)