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Mathematics - Circle Question with Solution | TestHub

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. For the separate condition $16 m^{2} - 8 l - 1 = 0$ , the equation of the circle having $l x + m y + 1 = 0$ as a tangent is

Options:

Answer:

Solution:

The stated condition gives $(4 l + 1)^{2} = 16 (l^{2} + m^{2})$ , so the tangent lines envelope the circle with centre $(4, 0)$ and radius 4: $(x - 4)^{2} + y^{2} = 16$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: QB

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