Question

If the equation 3x² + (3 – p)xy + qy² – 2px = 8pq represents a circle, find p and q. Also determine the centre and radius of the circle

Answer 1

3x² + (3 – p)xy + qy² – 2px = 8pq represent a circle means,

Co-efficient of x² = co-efficient of y²

3 = q

⇒ q = 3

Co-efficient of xy = 0

3 – p = 0

⇒ p = 3

3x² + 3y² – 6x = 8(3)(3)

3x² + 3y² – 6x – 72 = 0

(÷3) x² + y² – 2x – 24 = 0

2g = – 2

2f = 0

c = – 24

g = – 1 f = 0

Centre (– g, – f) = (1, 0)

Radius = `sqrt(g^2 + f^2 - "c")`

= `sqrt(1 + 0 + 24)`

= `sqrt(25)`

= 5