Does the point (1, square root 7) lie on the circle shown? explain

Yes, the distance from  to is  

Step-by-step explanation:

step 1

Find the equation of the circle

we know that

The equation of the circle is equal to

where

(h,k) is the center

r is the radius

In this problem we have

and the radius is equal to the distance between the center and the point

substitute in the equation

step 2

If the distance between the center and the point is equal to the radius of the circle , then the point lie on the circle

the formula to calculate the distance between two points is equal to

substitute the values

therefore

the point lie on the circle

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)