Question

If two diameters of a circle lie along the lines x − y = 9 and x − 2y = 7 and the area of the circle is 38.5 cm² , then find the equation of the circle.

Answer 1

Let the equation of the circle with centre (h, k) and radius ′′ be

(x− h)² + (y − k)² = r²    (1) 

The two diameters of the circle are 

x − y = 9       (2) 

x − 2y = 7       (3) 

Since the centre of a circle always lie on the diameter, so 

(2) ⇒ h− k = 9    (4) 

(3) ⇒ h − 2k = 7    (7)

(4) − (5) ⇒ k = 2 

(4) ⇒ h = 11 

∴ centre = (11, 2)

Also,

\(\pi r^2 = 38.5\)

∴ (1) ⇒ \({{(x-11)}^{2}}+{(y-2)^{2}}=\frac{49}{4}\)

, is the required equation of the circle