The slope of the tangent line of the circle
is
:
to find it we use implicit differentiation:
thus the slope of the tangent line at a point (x, y) of the circle is:
part a:
m at (0, 0) is (-0+3)/(0-4)=3/(-4)=-3/4
the equation of the tangent line is
(y-0)=(-3/4)(x-0)
y=(-3/4)x
part b)
The equation of the circle can be written in standard form by completing the square:
thus the circle has radius (3, 4) and radius 5.
part c.
the equation of the line is:
y-0=(3/4)(x-6)
y=(3/4)x-9/2
d) the lines are y=(-3/4)x and y=(3/4)x-9/2
they meet at x:
(-3/4)x=(3/4)x-9/2
(-6/4)x=-9/2
(6/4)x=9/2
(2/2)x=3/1
x=3,
at x=3, y=(-3/4)x=(-3/4)*3=-9/4
Check the graph, generated using desmos.com
Answer:
1/5
Step-by-step explanation:
Equation: 
Points: (-3, -9) and (22, -4)
is the second y point that shows up on the question, basically go by order. So it's -4
is -9, because again, in order of which coordinates pop-up first in the question
is 22, 
is -3
Now input into the equation, to make it easier we'll split the fraction into 2 equations:
= 
and 
, we'll put them back in a fraction later
= -4 - (-9) = -4 + 9 = 5
= 22 - (-3) = 22 + 3 = 25
now put it in the fraction, remember y on top x on the bottom:
5/25, simplify, 1/5
The perimeter of a sector includes two segments that are each equal to the radius, and the arc length. For your sector, the arc length is found as
perimeter = 4r = r + r + arc-length
2r = arc-length
Now we also know that arc-length is related to the central angle (in radians) by
arc-length = r*central-angle
2r = r*central-angle
2 = central-angle
The measure of the central angle of the sector is 2 radians.
3^2 Is the answer. Which is the third option.
