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QJEEM22Ma308b: JEE Main 2022 Mathematics - Class 11 JEEM22Ma308b Solution: Let a circle C : (x − h) 2 + (y − k) 2 = r 2 , k > 0, touch the …

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 ___________.

Step-by-Step Verified Solution

JEE Main 2022 (Online) 24th June Evening Shift Mathematics - Circle Question 57 English Explanation

Here, OM2=OP2−PM2

(|1+r|2)2=r2−1

∴ r2−2r−3=0

∴ r=3

∴ Equation of circle is

(x−1)2+(y−3)2=32

∴ h = 1, k = 3, r = 3

∴ h+k+r=7

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