Question

Write the standard form of the equation of the circle with the given characteristics.
Center: (-3, 4); Radius: 3
4. [-/6 Points]
DETAILS
LARPCALC11 1.3.027.
Find the slope of the line passing through the pair of points. (If an answer does not exist, enter DNE.)
(-8, -12), (1, 24)

Answer 1

The standard form of the equation of the circle is (x+3)²+(y-4)²=9 .

The slope of the line is

A circle is defined as the locus of a moving point which is always equidistant from a given point.

• This given point is called the center of the circle.
• The distance between the center and the circumference of the circle is the radius if the circle.
• The standard form of a circle is given by the equation :                      (x-x₁)²+(y-y₁)²=r² , where (x₁,y₁) is a point on the circle and r is the radius.

The given point on the circle is  (-3, 4) and the radius is 3 units.

Hence the standard form of the equation of the circle is :

(x-{-3})²+(y-4)²=3²

or,  (x+3)²+(y-4)²=9

Let the two given two points as A(-8, -12) and B(1, 24).

Now the slope of the line AB can be calculated by the formula:

$m=\frac{y_2-y_1}{x_2-x_1}.$

Now let us put the given values in the equation to calculate slope:

$m_{AB}=\frac{24-(-12)}{1-(-8)}\\\\or, m_{AB}=\frac{36}{9} \\\\or, m_{AB}=4$

Hence the slope of the line is 4.

To learn more about circle visit:

https://brainly.com/question/23799314

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