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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleCommon tangents to two circlesMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q78-80: A circle C1 of radius r > 0 rolls externally around C2: x² + y² + 2rx = 0. Their line of centres has inclination 60° to the positive x-axis.

A circle $C_{1}$ of radius $r > 0$ rolls externally around $C_{2} : x^{2} + y^{2} + 2 r x = 0$ ; their line of centres has inclination $6 0^{\circ}$ to the positive $x$ -axis. Find the transverse common tangent at the point of contact.

Options:

Answer:

Solution:

The contact point is $(- r /2, r 3 /2)$ ; the tangent normal is $(1, 3)$ , so $x + 3 y - r = 0$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Common tangents to two circles

⏱ 2mℹ️ Source: QB

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