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Question 95 of 129

Q.If the circle has both x and y axes as tangents and has radius 1 unit then the equation of the circle is:

(a) (x+1)2+(y+1)2=1(x+1)^2 + (y+1)^2 = 1
(b) x2+(y−1)2=1x^2 + (y-1)^2 = 1
(c) (x−1)2+y2=1(x-1)^2 + y^2 = 1
(d) x2+y2=1x^2 + y^2 = 1
Puducherry TnboardTamil Nadu HSC First Year (DGE) Board 2018MCQ· 1mImportance★★★★★
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Tangency to the x-axis and y-axis both require the center's distance to each axis to equal the radius (1); only the circle centered at (−1,−1)(-1,-1) satisfies both.

A circle with center (h,k)(h,k) and radius rr is tangent to the x-axis when ∣k∣=r|k|=r, and tangent to the y-axis when ∣h∣=r|h|=r. Here r=1r=1, so we need ∣h∣=1|h|=1 and ∣k∣=1|k|=1, i.e. center at (±1,±1)(\pm1,\pm1).

  1. (x+1)2+(y+1)2=1(x+1)^2+(y+1)^2=1: center (−1,−1)(-1,-1), distances to both axes =1=r=1=r. Tangent to both. Valid.
  2. x2+(y−1)2=1x^2+(y-1)^2=1: center (0,1)(0,1), distance to y-axis =0≠1=0\ne1 — the circle crosses the y-axis, not tangent. Invalid. …
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