JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q27

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MathematicsInteger+4 / -1Question 27 of 90

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 $PQ$ is 2, then the value of $h+k+r$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 7

Circle. Touching the $x$ -axis at (1, 0) with $k>0$ : centre $(1,k)$ , $r=k$ .

Chord. Distance from the centre to $x+y=0$ is $\dfrac{1+k}{\sqrt2}$ ; half-chord 1 gives $k^2-\dfrac{(1+k)^2}2=1$ , i.e. $k^2-2k-3=0$ , $k=3$ .

Value. $h+k+r=1+3+3=7$ .

Answer: 7

Topics:Equation of a circle Distance of a point from a line

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JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 27