Question

If a circle passes through the point of
intersection of the coordinate axes with the
lines px – y + 1 = 0 and x – 2y + 3 = 0,
then the value of p is

Answer 1

Answer:

→ Let the lines cuts the x-axis at A and B.

Then,

OA = -1/p

&OB = -3

→ Also, let  the lines cut the y-axis at C and D.

Then,

⇒ OC = 1 & OB = 3/2

→ If the circle passes through A,B,C and D :

⇒ OA × OB = OC × OD

⇒ (-1/p )(-3) = 1 × 3/2

⇒ p=2.

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Answer 2

Answer:

→ Let the lines cuts the x-axis at A and B.

Then,

OA = -1/p

&OB = -3

→ Also, let  the lines cut the y-axis at C and D.

Then,

⇒ OC = 1 & OB = 3/2

→ If the circle passes through A,B,C and D :

⇒ OA × OB = OC × OD

⇒ (-1/p )(-3) = 1 × 3/2

⇒ p=2.

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