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Question
The sum of slopes of normal to all the standard parabolas i.e. y2=4ax,y2=−4ax,x2=4ay and x2=4ay at their respective parametric coordinate is
The sum of slopes of normal to all the standard parabolas i.e. y2=4ax,y2=−4ax,x2=4ay and x2=4ay at their respective parametric coordinate is
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Solution
The sum of slopes of normal to all the standard parabolas i.e. y2=4ax,y2=−4ax,x2=4ay and x2=4ay at their respective parametric coordinate is 0.
Since, slope for parabola y2=4ax is t,
For y2=−4ax slope is −t,
For x2=4ay slope is −1t
And, for x2=−4ay slope is 1t
So, on adding we get,
−t+t−1t+1t=0.
Since, slope for parabola y2=4ax is t,
For y2=−4ax slope is −t,
For x2=4ay slope is −1t
And, for x2=−4ay slope is 1t
So, on adding we get,
−t+t−1t+1t=0.
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