If (h,k) is the centre of a circle touching x−axis at a distance 3 units from the origin and makes an intercept of 8 units on the y−axis, then the equation of circle when (h+k) is maximum, is
A
(x−5)2+(y−3)2=25
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B
(x+5)2+(y+3)2=25
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C
(x+3)2+(y−5)2=25
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D
(x−3)2+(y−5)2=25
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Solution
The correct option is D(x−3)2+(y−5)2=25 Centre of the circle : C≡(3,k) Suppose circle cuts the y−axis at points A and B and M is the mid point of AB. Let us suppose diagram may be like
In △AMC, AC=r=|k| and AC2=AM2+CM2 ⇒r2=42+32 ⇒r2=25=k2 ⇒r=5,k=5,−5 For maximum value of (h+k) : k=5 ∴ Equation of circle is (x−3)2+(y−5)2=25