The Circle MATHS - The Circle

If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are:

1. (3, 1)
2. x = 4, y = 1
3. x = 8, y = 2
4. None of these

The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 is:

1. x² + y² - 6x - 6y + 9 = 0 
2. 4 (x² + y² - x - y) + 1 = 0
3. 4 (x² + y² + x + y) + 1 = 0
4. None of these

If the centroid of an equilateral triangle is (1, 1) and its one vertex is (-1, 2), then the equation of its circumcircle is:

1. x² + y² - 2x - 2y - 3 = 0
2. x² + y² + 2x - 2y - 3 = 0
3. x² + y² + 2x + 2y - 3 = 0
4. None of these

The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x² - y² - 2x + 4y - 3 = 0, is:

1. x² + y² - 2x - 4y + 4 = 0
2. x² + y² + 2x + 4y - 4 = 0
3. x² + y² - 2x + 4y + 4 = 0
4. None of these

Write the area of the circle passing through (-2, 6) and having its centre at (1, 2).

Write the coordinates of the centre of the circle inscribed in the square formed by the lines x = 2, x = 6, y = 5 and y = 9.

If the radius of the circle x² + y² + ax + (1 - a) y + 5 = 0 does not exceed 5, write the number of integral values a.

If the line y = mx does not intersect the circle (x + 10)² + (y + 10)² = 180, then write the set of values taken by m.

Find the equation of the circle passing through the point of intersection of the lines x + 3y = 0 and 2x - 7y = 0 and whose centre is the point of intersection of the lines x + y + 1 = 0 and x - 2y + 4 = 0.

Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x + 5y = 18.

Find the equation of the circle which touches the axes and whose centre lies on x - 2y = 3.

Find the equation of the circle passing through the points:
(5, 7), (8, 1) and (1, 3)

Find the equation of the circle passing through the points:
(0, 0), (-2, 1) and (-3, 2)

Find the equation of a circle,
Passing through the origin, radius 17 and ordinate of the centre is -15.

Find the equation of a circle,
Which touches x-axis at a distance 5 from the origin and radius 6 units.

Prove that the radii of the circles x² + y² = 1, x² + y² - 2x − 6y - 6 = 0 and x² + y² - 4x - 12y - 9 = 0 are in A.P.

Find the equations of the circles passing through two points on y-axis at distances 3 from the origin and having radius 5.

The circle x² + y² - 2x - 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.

Prove that the radii of the circles x² + y² = 1, x² + y² - 2x − 6y - 6 = 0 and x² + y² - 4x - 12y - 9 = 0 are in A.P.

The circle x² + y² - 2x - 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.