- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

A trapezium is inscribed in the parabola y[itex]^{2}[/itex]=4x such that its diagonal pass through the point (1,0) and each has length 25/4. Find the area of trapezium.

## Homework Equations

Length of chord is given by

(4/m[itex]^{2}[/itex])([itex]\sqrt{1+m^{2}}[/itex][itex]\sqrt{a(a-mc)}[/itex]

Here a=1 and m is an unknown quantity

Equation of focal chord

(t[itex]_{1}[/itex]+t[itex]_{2}[/itex])y=2(x-1)

## The Attempt at a Solution

The length of the chord is given. Also from the equation of focal chord c=-2/t[itex]_{1}[/itex]+t[itex]_{2}[/itex] which is m. So in my first equation the only unknown quantity is m and equating it to (25/4) yields a biquadratic equation. Now finding m from here is very difficult and laborious too as the roots are not in whole numbers. Also if I find m with much difficulty(I will need a computer to get the roots lol) I have one more step to go which is to find the 4 points which I assume will take a lot of time. But nevertheless if anyhow I manage to find those 4 points I still have one more step to go before I reach the final answer and that is calculation of area which is just impossible to calculate manually. There must be some other and easier way to do this because if it would have been this difficult no one would solve it.