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MathematicsCircleTangent & NormalMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

For a family of lines lx + my + 1 = 0, the condition 7l² - 9m² + 8l + 1 = 0 describes tangents to a circle with centre (4, 0) and radius 3. Use the separate condition in this question to find its requested circle.

If $7 l^{2} - 9 m^{2} + 8 l + 1 = 0$ , the line $l x + m y + 1 = 0$ is tangent to a circle with centre $(4, 0)$ and radius 3. If $4 l^{2} - 5 m^{2} + 6 l + 1 = 0$ , then the centre and radius of the circle having $l x + m y + 1 = 0$ as a tangent are

Options:

Answer:

Solution:

The separate condition gives $(3 l + 1)^{2} = 5 (l^{2} + m^{2})$ ; hence the circle has centre $(3, 0)$ and radius $5$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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