Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. (2 points)

Step-by-step explanation:

 Focus =(h,k+p)  

Directrix= y=k-p

Focus given is : (0,1)

And directrix given is : y=-1

(h,k+p) =(0,1)

On comparing the values we get

h=0 and k+p=1

y=k-p= -1

Hence, we gave two equations

k+p=1  and k-p= -1

Substitute p= 1-k in k-p= -1 we get:

k-(1-k) = -1

k-1+k= -1

k=0

Now, we get

h=0 and k=0

And put k=0 in p = 1-k

We get p=1

We have general equation of parabola

Hence, the required equation is :

c. (3,2,6) is the answer.

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.