Circle a is located at (6, 5) and has a radius of 4 units. what is the equation of a line that is tangent to circle a from point c (2, 8)?
a. x=2
b. y= -0.75x+9.5
c. y= 1.33x+1.66

answer:

  a.   x = 2

step-by-step explanation:

a graph can you answer this question.

the difference of x-coordinates of a and c is -4 units, so a vertical line through a will be tangent to the circle. (choice a).

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the difference of y-coordinates of a and c is 3 units, so the slope of the line from a to c is -3/4. that is, choice b describes a line through c that goes through the center of the circle. it cannot be tangent.

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the line y = 1.33x + 1.66 does not go through point c. it cannot be the required tangent, either.

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -