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Bogdan [553]
3 years ago
13

If the endpoints of the diameter of a circle are (8, −6) and (4, −2), what is the standard form equation of the circle?

Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0
We do the midpoint formula to find the center of the circle to get the left side of the equation.

Midpoint = [(X₁ + X₂) / 2 , (Y₁ + Y₂) / 2] 

Now plug in:

[(8 + 4) / 2 , (- 6 - 2) / 2]
(12 / 2 , - 8 / 2)
(6, - 4)

The center of the circle is (6, -4)

Now we plug it into the equation of a circle:

(x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius. 

(x - 6)² + (y + 4)² = r² is the left side of the equation. This will eliminate options A and C

Now we do the distance formula using the center and an endpoint to get the radius. The formula for distance is:

√((X₂ - X₁)² + (Y₂ - Y₁)²)

We plug in using either of the endpoints. 

√((4 - 6)² + (- 2 - (- 4))²)
√((-2)² + 2²)
√(4 + 4)
√8

√8 is your radius

(√8)² = 8

Your correct answer is (x - 6)² + (y + 4)² = 8, Option D
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Answer:

Szymborska's overall opinion of humanity in "A Contribution to Statistics" is overall positive

Step-by-step explanation:

Szymborska is a poet who likes to comment on society with irony and sarcasm.One example of this is when she splits people into categories in her poem “A Contribution to Statistics”. Here Szymborska’s overall opinion of humanity may seem negative due to her bluntness and dry humor. For example, she says in the tenth stanza, “cruel when forced by circumstances -better not to know even ballpark figures.” It’s implied in this line that most people (maybe even all)are cruel or can be. She also says, “taking only things from life -thirty”which comments how lots of people are selfish. However, this seemingly cynical poem takes a sweeter turn near the end with statistics like, “worthy of compassion - ninety-nine” and “mortal- a hundred out of a hundred.” These lines reveal that even though Szymborska believes that humanity is extremely flawed the mass majority of us deserve and are worthy of love. Plus the fact that we’re all mortal may seem dark but the fact remains that both the righteous and the sinners will all end up in the same place. The fact that no one can escape

death gives humans equality in a way. Szymborska’s overall opinion of humanity turned out to be more optimistic after all.

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