Question

a) Determine the equation of the circle center at the origin through A(-2;4).Draw a sketch
b)Determine the equation of the tangent to the circle at A.
c) This tangent cuts the x-axis at B. Determine the length of AB.
d) Determine the equation of the other tangent at the circle from B.

Answer 1

a) √-2^2+4^2
= √4+16
= √20

The general equation of a circle whose centre is (a,b) and radius r is:
(x-a)^2 + (y-b)2 = r2

Therefore, the equation is x2 + y2 = 20.

Answer 2

a) Equation is: x^2 + y^2 = 20

Answer 3

(a) as above, x^2+y^2 = 20
(b) dy/dx = -x/y
so (-2,4) the slope is 1/2, making the tangent line
y-4 = 1/2 (x+2)
(c) at B=(±√20,0) the length of AB is √((2±√20)^2+4^2)
(d) since y=0, the line is vertical: x=±√20