Ques. -17

Geometry Level 4

"A" is a point on the parabola $$y^2=4ax$$. The normal at A cuts the parabola again at B.

Statement-1: If AB subtends a right angle at the vertex of the parabola, then slope of AB is $$\frac{1}{\sqrt{2}}$$.

Statement-2: If normal at $$(at_1^2,2at_1)$$ cuts the parabola again at $$(at_2^2,2at_2)$$ , then $$t_2=-t_1-\frac{2}{t_1}$$.

Which of the following options is true ?

a). Statement-1 is true, Statement-2 is true. And statement-2 is a correct explanation of statement-1.

b). Statement-1 is true, Statement-2 is true. But Statement-2 is not correct explanation of statement-1.

c). Statement-1 is true, Statement-2 is false.

d). Statement-1 is false, Statement-2 is true.

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