Question

Q2If a double ordinate of the parabola y= 2ax is of length 4a, then the lines from the vertex to its two ends are at an angle ofOps: A. OoºB. O 90°c. o 60°D. 45°​

Answer 1

Answer:

If x=2at2,y2=(2at)2⟹y=±2at

WLOG the two ends be P(2ap2,2ap) and Q(2aq2,2aq)

So, the gradient of PQ will be

2a(q−p)2a(q2−p2)=1q+p

But it's perpendicular to the axis y=0 of the parabola

⟹q+p=0⟺q=−p

Now the length of PQ will be

(2ap2−2aq2)2+(2ap−2aq)2−−−−−−−−−−−−−−−−−−−−−−−−√=4a|q|

Finally, if O(0,0) is vertex, what will be product of gradients of OP,OQ?