If the curves $y^2=6 x, 9 x^2+b y^2=16$ intersect each other at right angles, the value of $b$ is

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Aicharya · Accepted Answer

$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}ight)_{C_1}=\frac{3}{y} 	ext { and }\left(\frac{\mathrm{d} y}{\mathrm{~d} x}ight)_{C_2}=\frac{-9 x}{b y}$ for orthogonal intersection $\left(\frac{\mathrm{d} y}{\mathrm{~d} x}ight)_{C_1} 	imes\left(\frac{\mathrm{d} y}{\mathrm{~d} x}ight)_{C_2}=-1$ $\begin{aligned} & \Rightarrow \frac{3}{y} 	imes \frac{-9 x}{b y}=-1 \ & \Rightarrow 27 x=b y^2 \ & \Rightarrow 27 x=b 	imes 6 x\left[\because y^2=6 xight] \ & \Rightarrow b=\frac{9}{2} \end{aligned}$

If the curves $y^2=6 x, 9 x^2+b y^2=16$ intersect each other at right angles, the value of $b$ is

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