Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaNormal to ParabolaMedium2 minQB

MathematicsMediuminteger

A line passing through $(21, 30)$ and normal to the curve $y = 2 x$ . If $m$ is slope of the normal then $m + 6 =$

Answer:

Solution:

Equation of the normal is $y = m x - 2 m - m^{3}$ If it pass through $(21, 30)$ we have $30 = 21 m - 2 m - m^{3} \Rightarrow m^{3} - 19 m + 30 = 0$ Then $m = - 5, 2, 3$ But if $m = 2$ or 3 then the point where the normal meets the curve will be $(a m^{2}, - 2 am)$ where the curve does not exist. Therefore $m = - 5$ $∴ m + 6 = 1$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Normal to Parabola

⏱ 2mℹ️ Source: QB

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