A tangent is drawn at any point P ( t ) on the parabola y 2 = 8 x and on it is taken a point Q ( α , β ) from which pair of tangents QA and QB are drawn to the circle x 2 + y 2 = 4 . The points from w

Question

A tangent is drawn at any point P ( t ) on the parabola y 2 = 8 x and on it is taken a point Q ( α , β ) from which pair of tangents QA and QB are drawn to the circle x 2 + y 2 = 4 . The points from which perpendicular tangents can be drawn both to the given circle and the parabola is/are

TestHub · Accepted Answer

Required point lies on the director circle of the given circle as well as on the directrix of the parabola ⇒ x 1 2 ​ + y 1 2 ​ = 8 and x 1 ​ + 2 = 0 ⇒ 4 + y 1 2 ​ = 8 ⇒ y 1 ​ = ± 2. ∴ Points are (-2, ±2).

Mathematics - Circle Question with Solution | TestHub

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