Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Homework 66 – Lines that Intersect Circles Directions: Complete this assignment on a separate sheet of paper. Be sure to show work. 1. Consider the circle centered at (−4, 4) with a radius of 15. a. Write the equation for the circle. b. Write the equations for the two vertical tangents to the circle. c. Write the equations for the two horizontal tangents to the circle. d. Where does the secant line with equation 𝑦 = −8 intersect the circle? e. Where does the secant line with equation 𝑦 = 𝑥 + 5 intersect the circle? f. Show that the point (−13, 16) is on the circle. g. Write the equation for a line tangent to the circle at −13, 16 . 2. Consider the circle with vertical tangents 𝑥 = −3 and 𝑥 = 7 and a horizontal tangent below the circle at 𝑦 = 1. a. Write the equation for the circle. b. Write the equation for the other horizontal tangent to the circle. c. Write the equation for a secant line that intersects the graph at 𝐴 −2, 9 and 𝐵 6, 3 . d. Find the midpoint of the chord formed by the secant line in part c. What is special about this chord? e. Write the equations for the lines tangent to the circle at points A and B from part c. 3. Consider the circle with a diameter that has endpoints −7, −8 and 9, 4 . a. Find the radius of the circle. b. Find the center of the circle. c. Write the equation of the circle. d. Find all the other integer value points on the circle. e. Write the equations for two vertical tangents. f. Write the equations for two horizontal tangents. g. Write the equation for two tangents that are neither horizontal nor vertical. 4