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.

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step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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