Question

The equation of the normal to the parabola $y^2=6x$ whose slope is ${}^{\prime }-1^{\prime }$, is

• A. $(x+y)=9/2$
• B. $x+y=9$
• C. $3(x+y)=4$
• D. $5(x+y)=9$

Answer 1

The correct option is A $(x+y)=9/2$

$y^2=6x,-t=m=-1,m=-1,t=1,a=\frac{3}{2}$

equation of normal to parabola

$\begin{array}{c}\Rightarrow y=mx-2am-a{m}^3\\ \Rightarrow y=-x+2\times \frac{3}{2}\times 1-\frac{3}{2}\times -1\\ \Rightarrow y=-x+3+\frac{3}{2}\\ \Rightarrow y=-x+\frac{9}{2}\\ x+y=\frac{9}{2}\end{array}$