Hello friends,
Is there a way to show that given a directrix of y=k and focus of (a,b), the lengths from focus to point on parabola and from point on parabola to directrix are same without actually deriving the parabola equation in directrix/focus form?
i was thinking about expressing some variables in terms of others and then showing that LHS=RHS, therefore lengths are similar.. But I cannot find a way to express variables differently.
thank you
Is there a way to show that given a directrix of y=k and focus of (a,b), the lengths from focus to point on parabola and from point on parabola to directrix are same without actually deriving the parabola equation in directrix/focus form?
i was thinking about expressing some variables in terms of others and then showing that LHS=RHS, therefore lengths are similar.. But I cannot find a way to express variables differently.
thank you