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Prove that the locus of the center of th...

Prove that the locus of the center of the circle which touches the given circle externally and the given line is a parabola.

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To prove that the locus of the center of a circle that touches a given circle externally and a given line is a parabola, we can follow these steps: ### Step 1: Understand the Problem Let’s denote the given circle as \( C_1 \) with center \( O(0, 0) \) and radius \( a \). Let the given line be \( L: x = b \), where \( b \) is a constant. We need to find the locus of the center \( P(h, k) \) of a circle \( C_2 \) that touches both \( C_1 \) and line \( L \). **Hint:** Visualize the situation by drawing the circle and the line. ### Step 2: Set Up the Equations ...
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