Using a directrix of y = −2 and a focus of (1, 6), what quadratic function is created?

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)

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

step-by-step explanation: