The condition that the chord x cos α+y sin α-p=0 of x2+y2-a2=0 may subtend a right angle at the center of the circle is

Question

The condition that the chord x cos α+y sin α-p=0 of x2+y2-a2=0 may subtend a right angle at the center of the circle is (A) a2=2 p2 (B) p2=2 a2 (C) a=2 p (D) p=2 a

Tardigrade Admin · Accepted Answer

The distance of the given line from the center of the circle is |p|. Now, the line subtends right angle at the center. Hence, Radius =√2|p| or a=√2|p| or a2=2 p2

Q. The condition that the chord $x cos α + y sin α - p = 0$ of $x^{2} + y^{2} - a^{2} = 0$ may subtend a right angle at the center of the circle is

$a^{2} = 2 p^{2}$

$p^{2} = 2 a^{2}$

$a = 2 p$

$p = 2 a$

The distance of the given line from the center of the circle is $∣ p ∣$ .
Now, the line subtends right angle at the center. Hence,
Radius $= 2 ∣ p ∣$
or $a = 2 ∣ p ∣$
or $a^{2} = 2 p^{2}$

Q. The condition that the chord xcosα+ysinα−p=0 of x2+y2−a2=0 may subtend a right angle at the center of the circle is

a2=2p2

p2=2a2

a=2p

p=2a