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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