Question

If the normal at point P (at12,2at1) and Q(at22,2at2) on the parabola y2=4ax meet on the parabola, thet1t2 equals

Answer 1

Explanation:
Given: Normals at P and Q at the points (at12,2at1) and (at22,2at2) respectively meet the parabola y2=4ax
We have to find the value of t1t2.
Let normal at P meets on the parabola
y2=4ax at (at2,2at)..
then, by the property of normal to the parabola we have,
T=−t1−2t1 .......(i)
Similarly, normal at Q meets on the parabola
y2=4ax at (at2,2at)
So, T=−t2−2t2....(ii)
Using (i) and (ii), we get
⇒t1−2t1=−t2−2t2(t2−t1)=2(1t1−1t2)
⇒t1t2=2[∵t1≠t2]
Hence, the correct answer is 2.00.