Mathematics - Circle Question with Solution | TestHub

MathematicsCircleRadical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circlesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q60-62: A coaxial system is a family of circles sharing one radical axis. Limiting points are its zero-radius point circles.

A coaxial system is a family of circles with the same radical axis. Its limiting points are the zero-radius point circles in the family. Find the circle through the origin in the coaxial system with limiting points (1, -1) and (2, 0).

Options:

Answer:

Solution:

The point-circle pencil $[(x - 1)^{2} + (y + 1)^{2}] + λ [(x - 2)^{2} + y^{2}] = 0$ passes through the origin when $2 + 4 λ = 0$ . Normalising gives $x^{2} + y^{2} + 4 y = 0$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Radical Axis & Radical Centre, Coaxial system of circles, Orthogonality of two circles

⏱ 2mℹ️ Source: QB

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