Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Human Impact PSA Project.doc
Assignment name: Unit 3 Learnit
https://apclassroom.collegeboard.org/114/assessments/assignments/57312614
Q
A
(1)
母CollegeBoard
Pre-AP
Unit 3 Learning Checkpoint 2
2
3
4
(5)
(6)
(7)
(8)
(9)
(10)
(11)
The circle with center 
A and radius 
bar(AB) is shown in the 
xy plane. The circle has equation 
(x-3)^(2)+(y-3)^(2)=13. Which of the following is the equation of the tang the circle at point 
B ?
(A) 
y=(2)/(3)x+(16)/(3)
(B) 
y=(2)/(3)x+5
(c) 
y=(3)/(2)x+(9)/(2)
(D) 
y=-(3)/(2)x+(pi)/(2)
9 sep soo
Search

Human Impact PSA Project.doc\newlineAssignment name: Unit 33 Learnit\newlinehttps://apclassroom.collegeboard.org/114114/assessments/assignments/5731261457312614\newlineQ\newlineA\newline(11)\newline母CollegeBoard\newlinePre-AP\newlineUnit 33 Learning Checkpoint 22\newline22\newline33\newline44\newline(55)\newline(66)\newline(77)\newline(88)\newline(99)\newline(1010)\newline(1111)\newlineThe circle with center A A and radius AB \overline{A B} is shown in the xy x y plane. The circle has equation (x3)2+(y3)2=13 (x-3)^{2}+(y-3)^{2}=13 . Which of the following is the equation of the tang the circle at point B B ?\newline(A) y=23x+163 y=\frac{2}{3} x+\frac{16}{3} \newline(B) y=23x+5 y=\frac{2}{3} x+5 \newline(c) y=32x+92 y=\frac{3}{2} x+\frac{9}{2} \newline(D) y=32x+π2 y=-\frac{3}{2} x+\frac{\pi}{2} \newline99 sep soo\newlineSearch

Full solution

Q. Human Impact PSA Project.doc\newlineAssignment name: Unit 33 Learnit\newlinehttps://apclassroom.collegeboard.org/114114/assessments/assignments/5731261457312614\newlineQ\newlineA\newline(11)\newline母CollegeBoard\newlinePre-AP\newlineUnit 33 Learning Checkpoint 22\newline22\newline33\newline44\newline(55)\newline(66)\newline(77)\newline(88)\newline(99)\newline(1010)\newline(1111)\newlineThe circle with center A A and radius AB \overline{A B} is shown in the xy x y plane. The circle has equation (x3)2+(y3)2=13 (x-3)^{2}+(y-3)^{2}=13 . Which of the following is the equation of the tang the circle at point B B ?\newline(A) y=23x+163 y=\frac{2}{3} x+\frac{16}{3} \newline(B) y=23x+5 y=\frac{2}{3} x+5 \newline(c) y=32x+92 y=\frac{3}{2} x+\frac{9}{2} \newline(D) y=32x+π2 y=-\frac{3}{2} x+\frac{\pi}{2} \newline99 sep soo\newlineSearch
  1. Circle Equation Given: The equation of the circle is given by (x3)2+(y3)2=13(x-3)^2 + (y-3)^2 = 13. The center of the circle is at point A with coordinates (3,3)(3,3) and the radius is 13\sqrt{13}.
  2. Find Slope of Radius: To find the equation of the tangent line at point BB, we need the slope of the radius at point BB, because the tangent line is perpendicular to the radius at the point of tangency.
  3. Use Perpendicularity Property: The slope of the radius can be found using the derivative of the circle's equation. However, since we don't have the coordinates of point BB, we can't directly find the slope of the tangent line. Instead, we'll use the fact that the product of the slopes of two perpendicular lines is 1-1.
  4. Calculate Slope of Tangent: Let's assume the slope of the radius ABAB is m1m_1. Then the slope of the tangent line at BB, m2m_2, would be 1/m1-1/m_1 because m1m2=1m_1 \cdot m_2 = -1.
  5. Find Coordinates of Point B: We can find m1m_1 by drawing a line from the center AA to point BB and using the coordinates of AA. If BB lies on the circle, it satisfies the circle's equation. Let's assume BB has coordinates (x1,y1)(x_1, y_1).
  6. Alternative Approach: Since we don't have the exact coordinates of BB, we can't find the exact slope m1m_1. We need another approach to find the slope of the tangent line.

More problems from Reflections of functions