1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
spin [16.1K]
2 years ago
14

Circle B has a center at point (0, 2) and a point W on the circle at (3, 3). Which equation represents a line that is tangent to

the circle and goes through the point W?
Mathematics
1 answer:
Solnce55 [7]2 years ago
5 0

According to the given information, the equation represents a line that is tangent to the circle and goes through the point W is given by:

y = -x + 6.

<h3>What is the equation of the circle?</h3>

The equation of a circle of center (x_0,y_0) and radius r is given by:

(x - x_0)^2 + (y - y_0)^2 = r^2

In this problem, we have that the center is at point (0,2), hence:

x^2 + (y - 2)^2 = r^2

It goes through point (3,3), hence:

3^2 + (3 - 2)^2 = r^2

r^2 = 10

Hence, the equation is:

x^2 + (y - 2)^2 = 10

<h3>What is the equation of the tangent line at point W?</h3>

It is given by:

y - y(0) = \frac{dy}{dx}|_{W}(x - x(0))

Applying implicit differentiation, we have that:

2x + 2y\frac{dy}{dy} = 0

\frac{dy}{dx} = -\frac{x}{y}

Point W(3,3), hence:

(x_0, y_0) = (3,3)

\frac{dy}{dx} = -\frac{3}{3} = -1

Hence the equation is:

y - 3 = -(x - 3).

y = -x + 6.

More can be learned about the equation of a tangent line at brainly.com/question/8174665

You might be interested in
Which function represents the graph of h(x)=2|x+3|−1 after it is translated 2 units right?
harina [27]

\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}

\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}

\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}

now with that template in mind

\bf h(x)=\stackrel{A}{2}|\stackrel{B}{1}x+\stackrel{C}{3}|\stackrel{D}{-1}\qquad \qquad \stackrel{\textit{C=C-2 a translation to the right}}{h(x)=2|x\boxed{+3-2}|-1} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill h(x)=2|x+1|-1~\hfill

8 0
3 years ago
Read 2 more answers
The value of 7y–2 is 10 more than the value of 2y
const2013 [10]

Answer:

y=12/5 (in decimal notation y=2.4)

Step-by-step explanation:

the value of 7y-2 = 10 more than 2y

7y-2 = 10+2y

7y-2y = 10+2

5y = 12

y = 12/5

y = 2.4

3 0
3 years ago
Encuentra la ecuacion de la parabola con vertice en el origen y foco en las cordenadas 0,1en su forma ordinaria y general
marusya05 [52]

Answer:

x^{2}=4y

y=\frac{1}{4}x^{2}

Step-by-step explanation:

Forma ordinaria

La ecuación de la parabola de manera ordinaria está dada por:

(x-h)^{2}=4p(y-k) (1)  

Donde:

  • (h,k) es la coordenda del vértice, en nuestro caso (0,0) ya que está en el origen.
  • (h,k+p) es la coordenda del foco, en nuestro caso (0,1).

Por lo tanto h = 0, k = 0 y p = 1.

Remplazando estos valores en la ecuación de la parábola, tenemos:

(x-0)^{2}=4*1(y-0)

x^{2}=4y (2)

 

Forma general  

La forma general de una parábola esta dada por la siquiente ecuación

y=ax^{2}+bx+c

Reordenando la ecuación (2) tenemos:

y=\frac{1}{4}x^{2}

Espero esto te haya ayudado!

5 0
3 years ago
Answer asap 50 point's brainlyest.
Anni [7]

Answer:

Option B

The answer is 16

Step-by-step explanation:

<h3><u>Given</u>;</h3>
  • 4(v – 13) = 12
<h3><u>To </u><u>Find</u>;</h3>
  • The value of v

Now,

4(v – 13) = 12

4(v – 13)/4 = 12/4

v – 13 = 3

v – 13 + 13 = 3 + 13

v = 16

Thus, The value of v is 16

<u>-TheUnknownScientist 72</u>

8 0
2 years ago
Read 2 more answers
padma works at an electronics store. in addition to her salary, she receives 2 percent of the sales dollars she brings in each m
11111nata11111 [884]

Answer:

Step-by-step explanation:

A Commission

7 0
8 months ago
Other questions:
  • The fastest a human has ever run is 27 miles per hour how many miles per minute did the human run
    9·1 answer
  • What is 46 percent of 22
    15·1 answer
  • Erica has 7 square feet of garden space to plant carrots,beans,peppers,and lettuce.If she gives each vegetable an equak amount o
    15·1 answer
  • HELP!!!!
    12·1 answer
  • I’m just starting to watch the vampire diaries. SO TELL ME EVERYTHING I need to know btw I’m on the episode pilot. NO SPOILERS!
    11·1 answer
  • . (3, 6) and (6,9)<br> slope of the line
    5·1 answer
  • (07.03)
    10·2 answers
  • Ms. Bohannon has 45 students in her 6th grade class. There is a ratio of boys to girls is 5 to 6. Which number could be the numb
    9·2 answers
  • Can someone plz help me I’m stuck on this one
    11·1 answer
  • Adam had $27 to spend on 3 beakers for his science class. After buying them, Adam had $6 left. How much did each of the beakers
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!