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प्रश्न
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
उत्तर
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
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