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A circle with center (4, -5) is tangent to the y-axis in the standard (x, y) coordinate plane. What is the radius of this circle?

A circle with center (4, -5) is tangent to the y-axis in the standard (x, y) coordinate plane. What is the radius of this circle? Correct Answer 4

Concept:

Equation of circle with center at (h, k) and radius r units is given by: (x - h)2 + (y - k)2 = r2.

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Calculation:

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Here, (h, k) = (4, -5) and let the radius be r units.

The equation of the required circle is

(x - 4)2 + (y + 5)2 = r2

Since, y-axis is the tangent to the circle

So, The coordinates of the point common to the circle and the tangent y-axis is (0, -5).

So, The point (0, -5) will satisfy the equation of the circle.

⇒ (0 - 4)2 + (-5 + 5)2 = r2

⇒ r = 4

Hence, The radius of the circle is 4 units.

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