Find the secant line to the unit circle that is equidistant from the $x$-axis
Answer 1
William King
To find the secant line to the unit circle that is equidistant from the $x$-axis, we use the equation of the unit circle
$ x^2 + y^2 = 1 $
and the general equation of a line
$ y = mx + b $
Since the secant line is equidistant from the $x$-axis, the $y$-intercept $b$ must satisfy the condition that the distances from $b$ to the points of intersection with the circle are equal. So, we solve:
Substitute $y = mx + b$ into the circle
Answer 2
Lily Perez
To find the secant line to the unit circle that is equidistant from the $x$-axis, use the circle equation
$ x^2 + y^2 = 1 $
and the line equation
$ y = mx + b $
Substitute $y = mx + b$ into the circle
Answer 3
Thomas Walker
For a secant to the unit circle
$ x^2 + y^2 = 1 $
and line
$ y = mx + b $
the intersection condition is:
$ b^2 < 1 + m^2 $
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