How do you find all points on the y-axis of a Cartesian coordinate system that are 13 units from the point (12,0)?

Answer 1

To find all points on the y-axis that are 13 units from the point (12,0), we can use the distance formula. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) = (12, 0) and we want to find the points on the y-axis, so the x-coordinate will be 0. Let's substitute these values into the distance formula:

13 = √((0 - 12)^2 + (y2 - 0)^2)

Simplifying the equation:

169 = 144 + y2^2

Subtracting 144 from both sides:

25 = y2^2

Taking the square root of both sides:

±5 = y2

Therefore, the points on the y-axis that are 13 units from the point (12,0) are (0, 5) and (0, -5).

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Answer 2

Isaiah Anthony

Points on the circle #(x-12)^2+y^2= 13^2#

The locus of (x, y) that is at the same distance a from #(alpha, beta)

is the circle

#(x-alpha)^2+y-beta)^2=a^2#

Here, #alpha = 12, beta = 0 and a = 13#.

See the graph.

graph{(x-12)^2+y^2-13^2=0 [-30.87, 30.88, -15.44, 15.43]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.