Answer:
R(17, 0)
Step-by-step explanation:
You want the coordinates of the point R on the x-axis where a tangent to the circle x²+y²=17 meets the circle at P with an x-coordinate of 1.
Secant-tangent relation
If A and B are the points on the x-axis where the circle meets it, the relation between secants and tangents tells us ...
(RA)(RB) = (RP)²
The point P has x-coordinate 1. Its y-coordinate will satisfy ...
x² +y² = 17
y² = 17 -1² = 16
y = ±4
The distances from point R=(x, 0) to points A, B, and P can be found using the distance formula, or by subtracting x-coordinates.
[tex](RA)(RB)=(RP)^2\\\\(x-(-\sqrt{17}))(x -\sqrt{17})=(x-1)^2+(0-(4))^2\\\\x^2-17=x^2-2x+17\\\\2x=34\\\\x=17[/tex]
The point R is (17, 0), verified by the geometric construction shown in the attachment.
