Human Impact PSA Project.docAssignment name: Unit 3 Learnithttps://apclassroom.collegeboard.org/114/assessments/assignments/57312614QA(1)母CollegeBoardPre-APUnit 3 Learning Checkpoint 2234(5)(6)(7)(8)(9)(10)(11)The circle with center A and radius 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=32x+316(B) y=32x+5(c) y=23x+29(D) y=−23x+2π9 sep sooSearch
Q. Human Impact PSA Project.docAssignment name: Unit 3 Learnithttps://apclassroom.collegeboard.org/114/assessments/assignments/57312614QA(1)母CollegeBoardPre-APUnit 3 Learning Checkpoint 2234(5)(6)(7)(8)(9)(10)(11)The circle with center A and radius 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=32x+316(B) y=32x+5(c) y=23x+29(D) y=−23x+2π9 sep sooSearch
Circle Equation Given: The equation of the circle is given by (x−3)2+(y−3)2=13. The center of the circle is at point A with coordinates (3,3) and the radius is 13.
Find Slope of Radius: To find the equation of the tangent line at point B, we need the slope of the radius at point B, because the tangent line is perpendicular to the radius at the point of tangency.
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 B, 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.
Calculate Slope of Tangent: Let's assume the slope of the radius AB is m1. Then the slope of the tangent line at B, m2, would be −1/m1 because m1⋅m2=−1.
Find Coordinates of Point B: We can find m1 by drawing a line from the center A to point B and using the coordinates of A. If B lies on the circle, it satisfies the circle's equation. Let's assume B has coordinates (x1,y1).
Alternative Approach: Since we don't have the exact coordinates of B, we can't find the exact slope m1. We need another approach to find the slope of the tangent line.