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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2007

MathematicsEasysingle choice

The curve described parametrically by $x = t^{2} + 2 t - 1, y = 3 t + 5$ represents

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Solution:

$Given x = t^{2} + 2 t - 1& y = 3 t + 5 \Rightarrow x = t^{2} + 2 t + 1 - 2& y = 3 t + 3 + 2 \Rightarrow x = (t + 1)^{2} - 2& y = 3 (t + 1) + 2 (2) \Rightarrow (t + 1) = x + 2 \dots\dots\dots (1)$ $∴$ Equation (2) becomes [using equation (1)] $y = 3 x + 2 + 2$ $\Rightarrow y - 2 = 3 x + 2$ $\Rightarrow y - 2 = 3 x + 2$ squaring both sides, we get squaring both sid $(y - 2)^{2} = 9 (x + 2)$ $\Rightarrow Y^{2} = 9 X$ where $Y = y - 2& X = x + 2$ This equation represents a parabola

Stream:VITEEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2007

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