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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For Q55-56: The lines ℓx + my + 1 = 0 satisfy 4ℓ² - 5m² + 6ℓ + 1 = 0 and are tangent to one fixed circle.

If $4 ℓ^{2} - 5 m^{2} + 6 ℓ + 1 = 0$ , then $ℓ x + m y + 1 = 0$ is tangent to a fixed circle. Find the centre and radius of that circle.

Options:

Answer:

Solution:

The condition is $(3 ℓ + 1)^{2} = 5 (ℓ^{2} + m^{2})$ , equivalent to tangency of $ℓ x + m y + 1 = 0$ to the circle centred at $(3, 0)$ with radius $5$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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