Find the equations of the circles whose radius is 5 and which passes t

1.	Find the equations of the circles whose radius is 5 and which passes through the points on X-axis at distances 3 from the origin.
Answer» Given r = 5, passes through points on x-axis at a distance 3 from the origin ⇒ The points are (3,0) and (-3,0) Let x² + y² + 2gx + 2fy + c = 0 is required equation (3,0)6g + C + 9 = 0 … (1) (-3,0) -6g + C + 9 = 0 …. (2) r = 5; 25 = g² + f² -C Adding 1 and 2 we get c = -9 and g = 0 and f = ±4 ∴ The required equation is x² + y² + 8y – 9 = 0

Find the equations of the circles whose radius is 5 and which passes through the points on X-axis at distances 3 from the origin.

Answer»

Given r = 5, passes through points on x-axis at a distance 3 from the origin

⇒ The points are (3,0) and (-3,0)

Let x² + y² + 2gx + 2fy + c = 0 is required equation (3,0)6g + C + 9 = 0 … (1)

(-3,0) -6g + C + 9 = 0 …. (2)

r = 5; 25 = g² + f² -C

Adding 1 and 2 we get c = -9 and g = 0 and f = ±4

∴ The required equation is x² + y² + 8y – 9 = 0

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Find the equations of the circles whose radius is 5 and which passes through the points on X-axis at distances 3 from the origin.

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