Question

Find the point of intersection of the tangents to y²=4ax at the points whose coordinates are y1 and y2 .also show that the ordinate of the point of intersection is the A.M. of the ordinate of the points of contact​

Answer 1

Step-by-step explanation:

Let the coordinates of P and Q be (at

1

2

,2at

1

) and (at

2

2

,2at

2

) respectively.

Then y

1

=2at

1

and y

2

=2at

2

.

The coordinates of the point of intersection of the tangents at P and Q are (at

1

t

2

,a(t

1

+t

2

)).

∴y

3

=a(t

1

+t

2

)⇒y

3

=

2

y

1

+y

2

⇒y

1

,y

2

,y

3

are in A.P.