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What is the equation of circle which touches both the axes and has center on the line x + y = 2?1. x2 + y2 - 2x - 2y + 1 = 02. x2 + y2 + 2x + 2y + 1 = 03. x2 + y2 - 2x - 2y - 1 = 04. None of these.

Answer» Correct Answer - Option 1 : x2 + y2 - 2x - 2y + 1 = 0

Concept:

Equation of the circle having center at (h, k) and radius r is (x - h)2 + (y - k)2 = r2.

 

Calculation:

Let the centre of the circle on the line x + y = 2 be (a, 2 - a).

The circle will touch the x-axis and the y-axis at (a, 0) and (0, 2 - a) respectively.

Using the distance formula:

(2 - a)2 = a2 = r2

Now, the equation of the circle is (x - a)2 + (y - 2 + a)2 = r2 = a2.

Since, (a, 0) is a point on the circle, we must have:

02 + 4 + a2 - 4a = a2

⇒ a = 1

∴ The equation of the circle is (x - 1)2 + (y - 1)2 = 12.

⇒ x2 + y2 - 2x - 2y + 1 = 0.


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