find the locus of points of intersection of tangents drawn at the extremities of a focal chord of y^2=4x
Answers
Answered by
1
Hope this may help u for solving your problem
Attachments:
Answered by
0
Answer:
y
2
=a(x−3a)
Point of intersection of the normals drawn at the ends of a chord of y
2
=4ax is (x,y)=[a(t
1
2
+t
2
2
+t
1
t
2
+2),−at
1
t
2
(t
1
+t
2
)]
Since, for focal t
1
t
2
=−1
x=a(t
1
2
+t
2
2
+t
1
t
2
+2=a[(t
1
+t
2
)
2
−t
1
t
2
+2]=a[(t
1
+t
2
)
2
+3]
and y=−at
1
t
2
(t
1
+t
2
)=a(t
1
+t
2
)
eliminating t
1
+t
2
from x and y, we get
y
2
=a(x−3a)
Similar questions