Q65.Let A(1, 4) and B(1, −5) be two points. Let P be a point on the circle ((x −1))2 + (y −1)2 = 1 , such that (PA)2 + (PB)2 have maximum value, then the points, P, A and B lie on (1) a hyperbola (2) a straight line (3) an ellipse (4) a parabola xf(a)−af(x) equals:
What This Question Tests
The question requires finding a point on a circle that maximizes the sum of squares of distances to two fixed points. This involves using the Apollonius theorem and understanding how distance from the center of the circle affects maximization.
Concepts Tested
Formulas Used
Distance = sqrt((x2-x1)^2 + (y2-y1)^2)
(x-h)^2 + (y-k)^2 = r^2
PA^2 + PB^2 = 2(PM^2 + AM^2)
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📋 Question Details
- Chapter
- Circles
- Topic
- Geometric properties of a circle
- Year
- 2021
- Shift
- 26 Feb Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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