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Effectus [21]
2 years ago
5

I need help!!!!!!!!!!!

Mathematics
1 answer:
Tems11 [23]2 years ago
4 0

i) less than

ii) greater than

iii) less than

iv) greater than

Step-by-step explanation:

do you need the calculations too?

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A line is tangent to the circle x^2+y^2=41, at the point (-4,-5)
VashaNatasha [74]
If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
 A general circle's equation is (x-h)^2+(y-k)^2= r^2  
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)

Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0). 

The formula for slope is <u>Y1-Y2</u>
                                   X1-X2
We can break this down with our two points (center and tangent)
  (0,0)    and   (-4,-5)
(X1,Y1) and (X2,Y2)

therefore, we will put the equation as such
<u>0-(-5)= 5</u>  = <em> </em><u><em>5</em></u>
0-(-4)= 4     <em> 4</em>

<em>this is our slope from the center to the point of tangency.</em>

We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to. 

Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> =  <u>-5</u>  =  <u>-4</u><u>
</u>4     4        5   

Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.

Slope-int      y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept  ( the point where x=0, or where its on the y axis)

now we plug things in
(-4,-5) is our point,
<u>-4</u>  is our slope
5

-5=<u>-4</u>(-4)+b       After we plug things in, solve for b
     5

-5= 3.2+b

-1.8= b  or  b=  <u />1 <u>4</u>
                         5

Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u>  = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u>   5

<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em>     This is the equation of the tangent line</em><u>
</u><em>    5         5</em>


Hope that helped
7 0
3 years ago
On the coordinate plane, the four corners of Alejandro's garden are located at (0,2), (4,6), (8,2), and (4,-2). Which shape most
ohaa [14]
It is the shape of a rectangle

6 0
3 years ago
Read 2 more answers
HELP FOR BRAINLEST!!
Tju [1.3M]

Answer:

I believe D is the correct answer.

Step-by-step explanation:

8 0
2 years ago
Can someone help me solve this? What goes in the blank?<br><br> 38 47 56 65 __ 83 92
lesya692 [45]
74 because each number is increased by 9
7 0
3 years ago
Read 2 more answers
39. Solve for x. SHOW ALL WORK FOR FULL CREDIT m n 6x-4 112°​
coldgirl [10]

Answer:

x = 12

Step-by-step explanation:

6x - 4 and 112 are same- side interior angles and sum to 180° , that is

6x - 4 + 112 = 180

6x + 108 = 180 ( subtract 108 from both sides )

6x = 72 ( divide both sides by 6 )

x = 12

4 0
1 year ago
Read 2 more answers
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