# Ellipse chord joining two points subtends an angle identity can't understand the Ques

• Feb 27th 2009, 05:37 AM
Ellipse chord joining two points subtends an angle identity can't understand the Ques
Show that an equation of the chord joining the points P$\displaystyle (acos\omega, bsin\omega)$ and Q$\displaystyle (acos\theta, b sin\theta)$ on the ellipse with equation $\displaystyle b^2x^2+a^2y^2=a^2b^2$ is
$\displaystyle Bxcos\frac{1}{2}(\theta+\omega)+aysin{1}{2}(\theta +\omega)=abcos{1}{2}(\theta-\omega)$(SOLVED)

“Prove that, if the chord PQ subtends a right angle at the point (a,0), then PQ passes through a fixed point on the x-axis.”
The part in the quotation, I cannot understand what it demands, let alone do it. Will be gratified if somebody comes forward with a more graphic explanation. Help
• Feb 27th 2009, 06:55 AM
earboth
Quote:

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“Prove that, if the chord PQ subtends a right angle at the point (a,0), then PQ passes through a fixed point on the x-axis.”
The part in the quotation, I cannot understand what it demands, let alone do it. Will be gratified if somebody comes forward with a more graphic explanation. Help

I've attached a sketch of the situation. I've marked two different right angles at (a,0). All together there are drawn 11 right angles.

As you can see all chords intersect in one point on the x-axis. You are asked to calculate the coordinates of this point.

For the sketch I used a = 6, b = 4
• Feb 27th 2009, 07:35 AM
Quote:

Originally Posted by earboth
I've attached a sketch of the situation. I've marked two different right angles at (a,0). All together there are drawn 11 right angles.

As you can see all chords intersect in one point on the x-axis. You are asked to calculate the coordinates of this point.

For the sketch I used a = 6, b = 4

Is there any program you used, or did you do it by hand?
• Feb 27th 2009, 07:52 AM
earboth
Quote: