Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaTangent to ParabolaEasy2 minPYQ_2013

MathematicsEasysingle choice

If the line $2 x - 3 y = k$ touches the parabola $y^{2} = 6 x,$ then find the value of $k$

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Answer:

Solution:

$Given x = \frac{3 y + k}{2} and y^{2} = 6 x \Rightarrow y^{2} = 6 (\frac{3 y + k}{2}) \Rightarrow y^{2} = 3 (3 y + k) \Rightarrow y^{2} - 9 y - 3 k = 0 \dots\dots .. \dots\dots ..$ If line (1) touches parabola (2) then roots of quadratic equation ( 3 ) is equal $∴ (- 9)^{2} = 4 \times 1 \times (- 3 k) \Rightarrow k = - 27/4$

Stream:BITSATSubject:MathematicsTopic:ParabolaSubtopic:Tangent to Parabola

⏱ 2mℹ️ Source: PYQ_2013

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