The line 3 x − 2 = 2 y − 1 = − 1 z − 1 intersects the curve x 2 − y 2 = a 2 , z = 0 if a is equal to

Put z = 0 : 3 x − 2 = 2 y − 1 = 1 , so x = 5 , y = 3 . Then a 2 = 25 − 9 = 16 , so a = ± 4 .

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Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediummultiple choice

The line $\frac{x - 2}{3} = \frac{y - 1}{2} = \frac{z - 1}{- 1}$ intersects the curve $x^{2} - y^{2} = a^{2}, z = 0$ if $a$ is equal to

Answer:

A, C

Solution:

Put $z = 0 : \frac{x - 2}{3} = \frac{y - 1}{2} = 1$ , so $x = 5, y = 3$ . Then $a^{2} = 25 - 9 = 16$ , so $a = \pm 4$ .

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

⏱ 2mℹ️ Source: QB

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