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4. Let $P_1 = (x_1, y_1)$ and $P_2 = (x_2, y_2)$ be two points in the $(x, y)$-plane such that $y > 0$ and $x_1 < x_2$. We call a circle $C$ a Yeppeun circle for $P_1$ and $P_2$ if $C$ contains $P_1$ and $P_2$, $C$ is tangent to the $x$-axis at a point $P_3 = (x_3, 0)$, and the $x$-coordinate of the point of tangency lies between the $x$-coordinates of $P_1$ and $P_2$; that is, $x_1 < x_3 < x_2$. For example, the circle $C$ in the following diagram is a Yeppeun circle for the given $P_1$ and $P_2$ Given any two such points $P_1$ and $P_2$ above the $x$-axis, does a Yeppeun circle always exist? Explain.

          4. Let $P_1 = (x_1, y_1)$ and $P_2 = (x_2, y_2)$ be two points in the $(x, y)$-plane such that $y > 0$ and $x_1 < x_2$.

We call a circle $C$ a Yeppeun circle for $P_1$ and $P_2$ if $C$ contains $P_1$ and $P_2$, $C$ is tangent to the $x$-axis at a point $P_3 = (x_3, 0)$, and the $x$-coordinate of the point of tangency lies between the $x$-coordinates of $P_1$ and $P_2$; that is, $x_1 < x_3 < x_2$. For example, the circle $C$ in the following diagram is a Yeppeun circle for the given $P_1$ and $P_2$

Given any two such points $P_1$ and $P_2$ above the $x$-axis, does a Yeppeun circle always exist?
Explain.

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4. Let P1 = (x1, y1) and P2 = (x2, y2) be two points in the (x, y)-plane such that y > 0 and x1 < x2.

We call a circle C a Yeppeun circle for P1 and P2 if C contains P1 and P2, C is tangent to the x-axis at a point P3 = (x3, 0), and the x-coordinate of the point of tangency lies between the x-coordinates of P1 and P2; that is, x1 < x3 < x2. For example, the circle C in the following diagram is a Yeppeun circle for the given P1 and P2

Given any two such points P1 and P2 above the x-axis, does a Yeppeun circle always exist?
Explain.

Added by Michelle G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Sri K

06/21/2022

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This is because for a Yeppeun circle to exist, the x-coordinate of the point of tangency P3 must lie between the x-coordinates of P1 and P2, which may not always be possible depending on the positions of P1 and P2. Show more…

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Let P1=(x1,y1) and P2=(x2,y2) be two points in the (x,y)-plane such that y>0 and CP1P2CP1P2, CxP3=(x3,0)xxP1P2CP1P2P1P2xx1. For example, the circle C in the following diagram is a Yeppeun circle for the given P1 and P2 Given any two such points P1 and P2 above the x-axis, does a Yeppeun circle always exist? Explain. We call a circle C a Yeppeun circle for P1 and P2 if C contains P1 and P2, C is tangent to the x-axis at a point P3=(x3,0), and the x-coordinate of the point of tangency lies between the x-coordinates of P1 and P2; that is, x1. For example, the circle C in the following diagram is a Yeppeun circle for the given P1 and P2 Given any two such points P1 and P2 above the x-axis, does a Yeppeun circle always exist? Explain. Let P1=(x1,y) and P2=(x2,y) be two points in the (x,y)-plane such that y>0 and x1<2. We call a circle C a Yeppeun circle for P and P if C contains P and P2C is tangent to the r-axis at a point P3=(30and the -coordinate of the point of tangency lies between the -coordinates of P and P2;that is,1<<2.For example, the circle C in the following diagram is a Yeppeun circle for the given P and P2 Given any two such points Pi and P above the x-axis, does a Yeppeun circle always exist Explain.

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