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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediuminteger

If line $\frac{x - 2}{a} = \frac{y - b}{1} = \frac{z - 4}{4}$ meets the cylinder $x^{2} + y^{2} - 8 x + 2 y - 1 = 0$ at one point in xy plane, then maximum value of $(a + b)$ is

Answer:

Solution:

Use the given distance constraint and Cauchy-Schwarz. Equality is attainable: $P = (2 - a, b - 1, 0), (a + 2)^{2} + b^{2} = 18. a + b = (a + 2) + b - 2 \leq 2 ((a + 2)^{2} + b^{2}) - 2 = 36 - 2 = 4. a + 2 = b = 3, a = 1, b = 3. max (a + b) = 4 .$

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Line ( Equation etc.)

⏱ 2mℹ️ Source: QB

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