[calculus] the distance from the point (6, -4) to the circle is

(a) (b) 4 (c) 6 (d) 10 (e) none of these

Option C.

The distance from the point to the circle is 6 units

Step-by-step explanation:

we know that

The distance between the circle and the point will be the difference of the distance of the point from the center of circle  and the radius of the circle

step 1

Find the center and radius of the circle

we have

Convert to radius center form

Complete the square

Rewrite as perfect squares

so

The center is the point (0,4)

The radius is

step 2

Find the distance of the point from the center of circle

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

we have

(6,-4) and (0,4)

substitute the values

step 3

Find the difference of the distance of the point from the center of circle  and the radius of the circle

therefore

The distance from the point to the circle is 6 units

see the attached figure to better understand the problem

jfkc

step-by-step explanation:

jhcxzbfzc

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus