Question

Find the value of ‘p’ so that the equation x²+ y² − 2px + 4y − 12 = 0 may represent a circle of radius 5 units.

Answer 1

Given equation of the circle is x² + y² − 2px + 4y − 12 = 0 

⇒ (x²− 2px+ p² ) + (y² + 4 + 4) − p² − 4 − 12 = 0 

⇒ (x − p)² + (y + 2) ² = p² + 16

⇒(x − p)² + {y − (−2)}² = \(\sqrt{(p^2+16)^{2}}\)

∴ The center of the circle is (p, −2) and radius \(\sqrt{(p^2+16)}\) units

∴ Values of are 3 and -3