Write the equation of a circle whose center is at (3,-2) and has a radius of 11.Show your work!

Mathematics

1 answer:

Viefleur [7K]2 years ago

3 0

Answer:

$(x - 3)^{2} + (y + 2)^{2} = 121$

Step-by-step explanation:

The equation of a circle has the following format:

$(x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}$

In which r is the radius and the centre is the point $(x_{0}, y_{0})$

In this question:

Center at (3,-2), so $x_{0} = 3, y_{0} = -2$

Radius 11, so $r = 11$

Then

$(x - 3)^{2} + (y - (-2))^{2} = 11^{2}$

$(x - 3)^{2} + (y + 2)^{2} = 121$

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I NEED HELP ASAP<br> PLEASE

Sindrei [870]

We know that in order to solve a math problem, we need an equation. Luckily there's an equation to find the slope and intercept of a (straight) line!

Because of the equation:

Y = mx + b

You can use it to find the Y intercept, and then therefore slope (or the other way around)!

First, look at the point where the line meets with the y axis.

It's not clear, but it's 7.

That's your 'Y intercept'. Easy!

Then, to find the slope. There are a couple of ways to find it, but I'll show you the one using the y = mx + b equation.

In the equation, 'b' represents the Y intercept. Since we already know our Y intercept on the graph is 7, we can plug that into the equation.

Y = mx + 7

What's m? M is the slope of the line. In order to find this, we need more numbers to work with. Numbers from the line's coordinate points.

Since coordinates in a graph have x and y, we can plug in any coordinate from the graph's line into our equation (y = mx +7).

I choose...this point (points at random coordinate on line).

(3, 10) aka (x, y)

It's on the line, right? So it will be a reliable x and y.

Put the numbers in...

10 = 3m + 7

This looks a bit easier, right? Now we solve for m (the slope)!

Combine like terms.

10 - 7 = 3m

Divide the 3.

3/3 = m

m = 1.

That's your slope!

So, taking the solution, we can determine that the slope of the line is 1, and the intercept of the line is 7.

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Hope it helps! This is the most I can do for you :)

4 0

3 years ago

Determine the slope of the line that passes through the points:

miskamm [114]

Answer:

The slope of the line is 4.

Step-by-step explanation:

Recall that slope = rise over run: rise / run.

From the table we see that if x changes from 0 to 4, a run of 4, y changes from -1 to 15, a rise of 16, the slope of this line must be

m = rise / run = 16/4 = 4

The slope of the line is 4.

4 0

3 years ago

Line L passes through the points (1, 1) and (7, 8). What is the slope of a line that is perpendicular to line L?

asambeis [7]

When a line passes through the two points $(x_{1},y_{1}) and (x_{2},y_{2})$ , its slope is given by the formula $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

In this question, a line L passes through the points $(1,1) and (7,8)$

So, its slope is given by $m=\frac{8-1}{7-1}$

$m=\frac{7}{6}$

When two lines are perpendicular, then the product of their slopes is -1.

Since, the slope of the line L is $\frac{7}{6}$ , so the slope of the line which is perpendicular to the given line L is $\frac{-6}{7}$ as the product of $\frac{-6}{7} \times \frac{7}{6}=-1$ .