Find the points on the X-axis at a distance o | vedclass

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(A) Let the point on the $X$-axis be $P(x, 0)$.The distance between $P(x, 0)$ and $A(11, 12)$ is given as $13$.Using the distance formula: $\sqrt{(x -

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$(16, 0)$ and $(6, 0)$

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(A) Let the point on the $X$-axis be $P(x, 0)$.The distance between $P(x, 0)$ and $A(11, 12)$ is given as $13$.Using the distance formula: $\sqrt{(x - 11)^2 + (0 - 12)^2} = 13$.Squaring both sides: $(x - 11)^2 + (-12)^2 = 13^2$.$(x - 11)^2 + 144 = 169$.$(x - 11)^2 = 169 - 144 = 25$.Taking the square root: $x - 11 = \pm 5$.Case $1$: $x - 11 = 5 \implies x = 16$.Case $2$: $x - 11 = -5 \implies x = 6$.Therefore,the points are $(16, 0)$ and $(6, 0)$.

Find the points on the $X$-axis at a distance of $13$ from the point $(11, 12)$.

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