If a + b = s and a - b = t, then which of the following expresses the value of ab in terms of s and t? Please help me out

   =(s^2 - t^2)/4

Step-by-step explanation:

a + b = s and a - b = t,

Add the two equations together

a + b = s

a - b = t

2a = s+t

a = (s+t)/2

Subtract the two equations

a + b = s

- a + b = -t

2b =(s-t)

b = (s-t)/2

We want to find ab

ab = (s+t)/2 *  (s-t)/2

FOIL

    =(s^2 - t^2)/4

Answer : The center and radius of the circle is, (1, 3) and 6 respectively.

Step-by-step explanation :

The center-radius form of the circle equation in the format as:

where,

x and y are the variables.

h and k are the coordinates of circle.

r is the radius of circle.

As we are given the quadratic equation:

Now we have to convert this equation into center-radius form of the circle equation.

We are adding 1 and 9 on both side of equation.

As we know that,

So,

and,

Thus, the equation will be:

The center-radius form of the circle equation in the format as:

From this we conclude that,

h = 1

k = 3

As, r² = 36

So, r = 6

Center of the circle = (h, k) = (1, 3)

Radius of the circle = r = 6

Thus, the center and radius of the circle is, (1, 3) and 6 respectively.