Page 26 - Abstract book - TJSSF-2020

Thailand – Japan Student Science Fair 2020 (TJ-SSF 2020)
“Seeding Innovations through Fostering Thailand – Japan Youth Friendship”

X-intercept Distance for the Tangent Line of Circle and Ellipse

Shoko Yothee , Husna Aujeh
1
1
Advisor: Anan Chantarat

Princess Chulabhorn Science High School Satun
1
National Center for Genetic Engineering and Biotechnology, National Science and Technology
2
Development Agency, Pathumthani

Abstract

The purposes of this study were to find out the relationship between X-intercept distance of
tangent line with the distance from the center of the circle to the projection of the tangent points on the
circle and the radius of the circle. The relationship between X-intercept distance of tangent line with
the distance from the center of the ellipse to the projection of the tangent points on the ellipse and the
length of major axis and minor axis of the ellipse.

Performance shows that

1. For any circle, that there are the length of radius equal to r, the center is (0,0) , the tangent line
intersects the X-axis at (x2,0) and the projection of the tangent point on X-axis at (x1,0), we can conclude
that r = x1x 2
2
2. For any ellipse with parallel axes parallel to an X-axis, that there are the length of major axis equal
to r and the length of minor axis equal to s, the center is (0,0) , the tangent line intersects the X-axis at
(x2,0) and the projection of the tangent point on X-axis at (x1,0), we can conclude that r = x1x2
2
3. For any ellipse with parallel axes parallel to an Y-axis, that there are the length of major axis equal
to r and the length of minor axis equal to s, the center is (0,0) , the tangent line intersects the X-axis at
(x2,0) and the projection of the tangent point on X-axis at (x1,0), we can conclude that s = x1x 2
2

Keywords: X-intercept, Tangent line

14