Let α1 and α2 be the ordinates of two points A and B on a parabola y2=4 a x and let α3 be the ordinate of the point of intersection of its tangents at A and B. Then, α3-α2=

Question

Let α1 and α2 be the ordinates of two points A and B on a parabola y2=4 a x and let α3 be the ordinate of the point of intersection of its tangents at A and B. Then, α3-α2= (A) α3-α4 (B) α3+α1 (C) α1 (D) α1-α3

Tardigrade Admin · Accepted Answer

Ordinate of point of intersection of tangents at A and B whose ordinates are α1 and α2 is (α1+α2/2) So, α3=(α1+α2/2) 2 α3=α1+α2 ⇒ α3-α2=α1-α3

Q. Let $α_{1}$ and $α_{2}$ be the ordinates of two points $A$ and $B$ on a parabola $y^{2} = 4 a x$ and let $α_{3}$ be the ordinate of the point of intersection of its tangents at $A$ and $B$ . Then, $α_{3} - α_{2} =$

$α_{3} - α_{4}$

$α_{3} + α_{1}$

$α_{1}$

$α_{1} - α_{3}$

Ordinate of point of intersection of tangents at $A$ and $B$ whose ordinates are $α_{1}$ and $α_{2}$ is $\frac{α _{1} + α _{2}}{2}$
So, $α_{3} = \frac{α _{1} + α _{2}}{2}$
$2 α_{3} = α_{1} + α_{2}$
$\Rightarrow α_{3} - α_{2} = α_{1} - α_{3}$

Q. Let α1​ and α2​ be the ordinates of two points A and B on a parabola y2=4ax and let α3​ be the ordinate of the point of intersection of its tangents at A and B. Then, α3​−α2​=

α3​−α4​

α3​+α1​

α1​

α1​−α3​