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 length PQ equals ______ .
Answer:
12
Solution:
Subtracting the two circle equations gives 12x = 36, so x = 3 and y = 4 for A in the first quadrant. The line y = 4 meets C1 at x = ±3, so P = (-3, 4). It meets C2 where (x - 6)² = 9, so x = 3 or x = 9, hence Q = (9, 4). Therefore PQ = 12.
Stream:JEESubject:MathematicsTopic:CircleSubtopic:Chord, Intercept (Made by the circle)
⏱ 2mℹ️ Source: QB
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