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The endpoints of a diameter of a circle are (6,2) and (−2,5) . What is the standard form of the equation of this circle?

Paul [167]

Answer:

The standard form of the given circle is

$(x-2)^2+(y-\frac{7}{2})^2=73$

Step-by-step explanation:

Given that the end points of a diameter of a circle are (6,2) and (-2,5);

Now to find the standard form of the equation of this circle:

The center is (h,k) of the circle is the midpoint of the given diameter

midpoint formula is $M=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

Let $(x_{1},y_{1})$ and $(x_{2},y_{2})$ be the given points (6,2) and (-2,5) respectively.

$M=(\frac{6-2}{2},\frac{2+5}{2})$

$M=(\frac{4}{2},\frac{7}{2})$

$M=(2,\frac{7}{2})$

Therefore the center (h,k) is $(2,\frac{7}{2})$

now to find the radius:

The diameter is the distance between the given points (6,2) and (-2,5)

$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

$=\sqrt{(-2-6)^2+(5-2)^2}$

$=\sqrt{(-8)^2+(3)^2}$

$=\sqrt{64+9}$

$=\sqrt{73}$

Therefore the radius is $\sqrt{73}$

i.e., $r=\sqrt{73}$

Therefore the standard form of the circle is

$(x-h)^2+(y-k)^2=r^2$

Now substituting the center and radiuswe get

$(x-2)^2+(y-\frac{7}{2})^2=(\sqrt{73})^2$

$(x-2)^2+(y-\frac{7}{2})^2=73$

Therefore the standard form of the given circle is

$(x-2)^2+(y-\frac{7}{2})^2=73$

5 0

2 years ago

I am new here and I don't understand any of this :(

Scrat [10]

So, questions 1 through 3 are pretty vague and you can basically put whatever you think. But... as a hint you might want to base your answers to 1 through 3 on question 4, which is more specific and gives you some clues.

For example, question 2 asks "When do people usually need Kleenexes?" Question 4 basically answers this for you by saying "...blah blah blah are used throughout the duration of a cold." So you could easily say that people usually need Kleenexes when they are sick. You could use this same type of reasoning to answer questions 1 and 3.

To answer 4 itself you need to know how to use confidence intervals. Are you familiar with that?

Question 5 will be based off of your answer to question 4.

5 0

2 years ago

Read 2 more answers

Emily washes a car in 6 minutes. Larissa can wash that same car in 8

Arisa [49]

It takes Emily 6 minutes to wash the car. This means he washes 16
1
6
of the car per minute.Larissa therefore washes 18
1
8
of the car per minute. Working together, they both wash 16+18
1
6
+
1
8
of the car, or 724
7
24
of the car each minute. This means that it takes 247
24
7
minutes to wash the entire car — or 3 minutes, 25.714285... seconds total.

3 0

2 years ago

50 POINTS TIMED!! Which of the following shows the graph of y = 4x + 3? On a coordinate plane, an exponential function starts at

RoseWind [281]

Answer:

1st Graph

Step-by-step explanation:

Parent Graph of Exponentials: f(x) = a(b)^x + d

Since we are only modifying the base exponent and <em>d</em> (vertical movement), we should see that if we are only moving up and down, that graph 1 is the best choice.

Alternatively, we could graph the equation and choose the best fit:

5 0

2 years ago

Read 2 more answers

PLEASEE HELPPP!!!!

deff fn [24]

y = - $\frac{2}{5}$ x - 2

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 2x + 5y = 10 into this form

subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - $\frac{2}{5}$ x + 2 ← point- slope form with slope m = - $\frac{2}{5}$

Parallel lines have equal slopes hence

y = - $\frac{2}{5}$ x + c is the partial equation of the parallel line

to find c, substitute ( 5, - 4 ) into the partial equation

- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2

y = - $\frac{2}{5}$ x - 2 ← equation of parallel line

5 0

2 years ago