Let a circle C : x - h 2 + y - k 2 = r 2 , k 0 , touch the x -axis at 1 , 0 . If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord P Q is 2 , then the value of h + k + r is equal to _____.

Question

Let a circle C : x - h 2 + y - k 2 = r 2 , k > 0 , touch the x -axis at 1 , 0 . If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord P Q is 2 , then the value of h + k + r is equal to _____.,

MARKS App · Accepted Answer

Since the circle is touching x -axis so, k = r and h = 1 Now by diagram, O P = r , P R = 1 O R = r + 1 2 r 2 = 1 + r + 1 2 2 2 r 2 = 2 + r 2 + 1 + 2 r r 2 - 2 r - 3 = 0 r - 3 r + 1 = 0 r = 3 , - 1 h + k + r = 1 + 3 + 3 = 7

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