Question

The equation of a circle which passes through the three points (3,0) (1,-0),(4,-1)
(A) 2x + 2y + 5x -11y+ 3 = 0
(B) x² + y² - 5x +11y - 3 = 0
(C) x + y + 5x -11y + 3 = 0)
(D) 2x² + 2y? - 5x +11y - 3 = 0​

Answer 1

Answer:

The three points are given, the circle has to satisfy all the three points,'

I am taking the first point (3,0) and substituting in all the 3 equations , the first 3 equation doesn't satisfy the points, substituting the point in the final equation that is 2x² + 2y²- 5x+ 11y -3= 0

But the point (1,0) doesn't satisfy the above equation, so among the given equation of circles none of them passes through all the three points.

Answer 2

Answer:

x² + y² - 2x + 12y - 6 = 0

Step-by-step explanation:

Let the general equation of circle be

x² + y² + 2gx + 2fy + c = 0 ..... (1)

Since the circle passes through the points (3, 0), (- 1, 0) and (4, - 1), satisfying the equation (1) by these points, we get

3² + 0 + 2g (3) + 0 + c = 0

or, 6g + c + 9 = 0 ..... (2),

(- 1)² + 0 + 2g (- 1) + 0 + c = 0

or, 2g - c = 1 ..... (3)

and 4² + (- 1)² + 2g (4) + f (- 1) + c = 0

or, 8g - f + c + 17 = 0 ..... (4)

From (3), we get

c = 2g - 1 ..... (5)

Substituting c = 2g - 1 in (2), we get

6g + 2g - 1 + 9 = 0

or, 8g = - 8

or, g = - 1

Putting g = - 1 in (5), we get

c = 2 (- 1) - 1

or, c = - 2 - 1

or, c = - 3

From (4), we get

8 (- 1) - f - 3 + 17 = 0

or, - 8 - f - 3 + 17 = 0

or, f = 6

Therefore from (1), we get the required circle being

x² + y² - 2x + 12y - 6 = 0

Note: There's some incorrect data in the question. However the problem is solved using a conceived data. Check the method and I hope you find it helpful.