Question

a. the line y=7x cuts the circle x^2+y^2=50 at A and B. find the coordinates of A and B.

b. show that C(5;5) lies on the circle.

c. show that ACB angle C=90degrees. what can you deduce about AB?

d.find the equation of the tangent to the circle at C

Answer 1

nice problem:

b) the easiest, just sub in (5,5) to show it works

a) since y = 7x, sub the y into the circle equation
x^2 + (7x)^2 = 50
x^2 + 49x^2 = 50
x^1 = 1
x = ± 1

if x=1 , y = 7 , call that A(1,7)
if x = -1 , y = -7 , call that B(-1, -7)

c) slope AC = (5-7)/(5-1) = -2/4 = -1/2
slope BC = (5+7)/(5+1) = 12/6 = +2
since they are negative reciprocals of each other, they must form a 90° angle
AB must be a diameter of the circle.

d) slope of OC = (5-0)/(5-0) = 1
slope of the tangent must be -1
y-5 = -1(x-5)
y-5 = -x + 5
x+y = 10 is the tangent equation

Answer 2

thanks alot now I understand