Mathematics - Circle Question with Solution | TestHub
MathematicsCircleChord, Intercept (Made by the circle)Medium2 minQB
MathematicsMediuminteger
Passage / Comprehension
Circles C1: x² + y² = 25 and C2: (x - 6)² + y² = 25 intersect at A (in the first quadrant) and B. The line through A parallel to the x-axis meets C1 again at P and C2 again at Q.
The area of triangle PBQ equals ______ square units.
Answer:
48
Solution:
Subtracting the circle equations gives 12x = 36, so x = 3 and y = 4: A = (3, 4) and B = (3, -4). The line y = 4 meets C1 at x = ±3, so P = (-3, 4), and meets C2 where (x - 6)² = 9, so Q = (9, 4) (x = 3 is A). PQ = 12 and the distance from B to the line y = 4 is 8. Area = (1/2)(12)(8) = 48.
Stream:JEESubject:MathematicsTopic:CircleSubtopic:Chord, Intercept (Made by the circle)
⏱ 2mℹ️ Source: QB
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