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Most Important Selected Qs for JEE AdvancedMathematicsCircle

Tangents drawn from P(1,8) to the circle x^2+y^2-6 x-4 y-11=0 touches the circle at the points A and B respectively. If the radius of the circle which passes through the points of intersection of circles x^2+y^2-2 x-6 y+6=0 and x^2+y^2+2 x-6 y+6=0 and intersects the circumcircle of the P A B orthogonally is equal to p q where p, q N , then find the minimum value of (p+q) .

Correct answer

77

Step-by-step solution

Equation of circle circumscribing PAB is (x-1)(x-3)+(y-8)(y-2)=0 x^2+y^2-4 x-10 y+19=0 (i) As circle (ii) is orthogonal to circle (i), so -2 ( 2 -2 +1 )-5(-6)=19+6 2 ( 2 -2 +1 )=5 4 -4=5 +5 =-9 Hence required equation of circle is x^2+y^2+ 5 2 x-6 y+6=0 (ii) Radius = 25 16 +9-6 = 73 4 = p q p=73, q=4 Hence minimum value of (p+q)=73+4=77

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