Concept explainers
57. Refer to Problem 54. The line is tangent to a circle at . The line is tangent to the same circle at . Find the center of the circle.
To find: The center of the circle.
Answer to Problem 57AYU
Solution:
Explanation of Solution
Given:
is tangent to a circle at . The line is tangent to the same circle at .
Find the equation of the radius at .
Slope intercept of the point is . Hence its slope is .
We know that the radius and tangent line are perpendicular to each other at the point of tangency.
Recall that, product of slopes of perpendicular lines .
Therefore, slope of the radius line at is
Use point slope form, we can write the equation
Add on both sides
-----(1)
Find the equation of the radius at
Slope of is 2
Therefore the slope of the radius line at is
Using point slope form, we can write its equation is
Therefore
-----(2)
Then to find the center of the circle
Using equation (1) and (2) we get
and
Subtract (2) from (1)
Therefore, we get
Substitute in the equation (1) we get
There for the center of the circle is .
Chapter 1 Solutions
EBK PRECALC.:ENHANCED W/GRAPH.UTIL.
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