Question

The condition that the chord xcos(alpha)+ysin(alpha)-p=0 of x^2+y^2-a^2=0 may do subtend a right angle at the centre of the circle​

Answer 1

Answer:

Step-by-step explanation:

Since the circle's center lies on origin, hence the given chord can only subtend a right angle at the center if the chord is the hypotenuse of the quadrant right angled triangle formed by the chord and the circle in each quadrant.

Hence

x/(p/cosalpha) + y/(p/sinalpha) =1

Hence the chord intersects x axis at(p/cosalpha,o)  

and y axis is  (0,p/sinalpha)

Now both of these points has to satisfy the equation of the circle, since these points lie on the circumference of the circle.

These points are those points where the circle intersects the co-ordinate axes.

Hence by substituting, we get

p²=a²cos²α

p²=a²sin²α

By adding, we get

2p²=a²

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