JEE MAIN - Mathematics (2022 - 24th June Evening Shift - No. 22)
Let a circle C : (x $$-$$ h)2 + (y $$-$$ k)2 = r2, 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 PQ is 2, then the value of h + k + r is equal to ___________.
Answer
7
Explanation
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Here, $$O{M^2} = O{P^2} - P{M^2}$$
$${\left( {{{|1 + r|} \over {\sqrt 2 }}} \right)^2} = {r^2} - 1$$
$$\therefore$$ $${r^2} - 2r - 3 = 0$$
$$\therefore$$ $$r = 3$$
$$\therefore$$ Equation of circle is
$${(x - 1)^2} + {(y - 3)^2} = {3^2}$$
$$\therefore$$ h = 1, k = 3, r = 3
$$\therefore$$ $$h + k + r = 7$$
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