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Byju's Answer

Standard XII

Mathematics

Obtaining Centre and Radius of a Circle from General Equation of a Circle

If the circle...

Question

If the circles $x^{2} + y^{2} - 6 x - 8 y - 24$ = 0 and $3 x^{2} + 3 y^{2} + 2 g x + 2 f y + 0$ = 0 are concentric then (g.f)

(-9,-12)

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(-6,-8)

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(-3,-4)

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(9,12)

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Solution

The correct option is A
(-9,-12)

$x^{2} + y^{2} - 6 x - 8 y - 24$ = 0,centre of the circle= (3,4)

$3 x^{2} + 3 y^{2} + 2 g x + 2 f y + c$ = 0
Centre of the circle = $(\frac{- g}{3}, \frac{- f}{3})$
(g,f) = (-9,-12)

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If the circles x2+y2−6x−8y−24 = 0 and 3x2+3y2+2gx+2fy+0 = 0 are concentric then (g.f)

The correct option is A (-9,-12) x2+y2−6x−8y−24 = 0,centre of the circle= (3,4) 3x2+3y2+2gx+2fy+c = 0 Centre of the circle = (−g3,−f3) (g,f) = (-9,-12)

If the circles $x^{2} + y^{2} - 6 x - 8 y - 24$ = 0 and $3 x^{2} + 3 y^{2} + 2 g x + 2 f y + 0$ = 0 are concentric then (g.f)

The correct option is A
(-9,-12)

$x^{2} + y^{2} - 6 x - 8 y - 24$ = 0,centre of the circle= (3,4)

$3 x^{2} + 3 y^{2} + 2 g x + 2 f y + c$ = 0
Centre of the circle = $(\frac{- g}{3}, \frac{- f}{3})$
(g,f) = (-9,-12)