Find the value of k if the line 2y = 5x + k is a tangent to the parabola y² = 6x.

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2y = 5x + k

Yanam BieapBIEAP Intermediate Board 2025Subjective· 2mImportance★★★★★

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Write the line in $y=mx+c$ form and use the tangency condition $c=a/m$ for a line touching $y^2=4ax$ .

The parabola $y^2=6x$ has $4a=6$ , so $a=\dfrac{3}{2}$ .

The line $2y=5x+k$ can be written as $y=\dfrac{5}{2}x+\dfrac{k}{2}$ , so $m=\dfrac{5}{2}$ , $c=\dfrac{k}{2}$ .

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Q.Find the value of k if the line $2y = 5x + k$ is a tangent to the parabola $y^2 = 6x$ .