a) Centre (2,4), radius 5. x² + y² - 4x - 8y - 5= 0
b) centre (-3, -2) radius=6. x² + y² + 6x + 4y - 23= 0
c) centre (a, a), radius= a√2. x² + y² + 2ax - 2ay = 0
d) centre (acos k, a sin k) , radius= √(a² - b²). x² + y² - 2ax cos k - 2ay sin k = 0
e) centre (-a, -b) , radius= √(a² - b²).
x² + y² +2ax + 2by + 2b²= 0
f) centre at the origin and radius 4. x² + y² - 16 = 0
2) Find the centre and radius of each of the following:
a) (x -3)² + (y -1)²= 9. (3,1), 3
b) (x - 1/2)² + (y+ 1/3)²= 1/16. (1/2, -1/3), 1/4
c) (x + 5)² + (y - 3)²= 20. (-5,3), 2 √5
d) x ² + (y -1)²= 2. (0,1), √2
e) x² + y² - 4x + 6y= 5. (2,-3); 3√2
f) x² + y² - x + 2y= 3. (1/2,-); √17/2
3)a) Find the equation of the circle whose Centre is (2,-5) and which passes through the point (3,2). x² + y² - 4x + 10y - 21= 0
b) Find the equation of the circle whose Centre is (1,2) and which passes through the point (4,6). x² + y² - 2x - 4y - 20= 0
4)a) Find the equation of the circle radius 5 cm, whose centre lies on the y axis and which passes through the point (3,2). (x² + y²- 12y+11) or (x² + y² + 4y - 21= 0)
b) Find the equation of the circle whose centre lies on the positive direction of y axis at a distance 6 from the origin and whose radius is 4. x² + y²- 12y+20= 0
5)a) Find the equation of the circle whose centre is (2, -3) and which passes through the intersection of the line 3x + 2y = 11 and 2x + 3y = 4. x² + y² - 4x + 6y - 3= 0
b) Find the equation of the circle whose centre is (2, 3) and which passes through the intersection of the line 3x - 2y = 1 and 4x + y = 27. x² + y² - 4x - 6y - 12= 0
c) find the equation of the circle passing through the point (-1,3) and having its centre at the point of intersection of the lines x - 2y = 4 and 2x + 5y- 1 = 0. x² + y² - 4x + 2y - 20= 0
d) 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 - 2y + 4= and x + y + 1 = 0. x² + y² + 4x - 2y = 0
6)a) If two diameter of a circle lie along the lines x - y = 9 and x - 2y = 7 and the area of the circle is 38.5 sq.cm, find the equation of the circle. 4x² + 4y² - 88x - 16y +451= 0
b) If the equation of two diameters of a circle 2x + y= 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle. x² + y² - 16x + 20y + 64= 0
7) find the equation of the circle, the co-ordinate of the end points of one of whose diameters are:
a) A(3,2), B(2,5). x² + y² - 5x - 7y + 16= 0
b) A(5,-3), B(2,-4). x² + y² - 7x + 7y + 22= 0
c) A(- 2, -3) , B(-3,5). x² + y² + 5x - 2y - 9= 0
d) A(p,q), B(r,s). (x - p)(x - r)+ (y - q)(y - s) = 0
e) A(1,3) , B(4,5). Find also the equation of the perpendicular diameter. x² + y² - 5x - 8y +19= 0; 6x + 4y = 31
8) The sides of a rectangle are given by the equation x= -2, x = 4, y =- 2 and y = 5. Find the equation of circle drawn on the diagonal of this rectangle and as its diameter. x² + y² - 2x - 3y + 18= 0
9) Find the equation of a circle:
a) Which touches both the at a distance of 6 units from the origin. x² + y² - 12x - 12y + 36= 0
b) Which touches x-axis at a distance of 5 units from the origin and radius 6 units. x² + y² - 10x - 12y + 25= 0
c) Which touches both the axes and passes through the point (2,1). x² + y² - 2x - 2y + 1= 0, x² + y² - 10x - 10y +25= 0
d) passing through the origin, radius and ordinate of the centre is -15. x² + y² ±16x + 30y = 0
e) touches the axes and whose centre lies on x - 2y = 3. x² + y² +6x + 6y+ 9 = 0 or x² + y² - 2x + 2y +1 = 0
f) whose centre at the point (3,4) and touches the straight line on 5x + 12y = 1. 169(x² + y² - 6x - 8y)+ 381 = 0
g) radius 4 units touches the coordinates axes in the first quadrant. Find the equation of its images with respect to the line mirrors x= 0 and y= 0. x² + y² + 8x - 8y+ 16 = 0 ; x² + y² - 8x + 8y+ 16 = 0
h) touching y-axis at (0,3) and making an intercept of 8 units on the x-axis. x² + y² ± 10x - 6y+ 9 = 0
i) touching x-axis whose centre is (0, -4). x² + y² + 8y = 0
j) whose centre is at (3,4) and which touches the line 5x +12y = 1. 169(x² + y² -6x - 8y)+ 381 = 0
k) Which passes through the origin and cuts off intercept of length 'a', each from positive direction of the axes. x² + y² - ax - ay = 0
l) centre is (a, b) and which passes through the origin. x² + y² - 2ax - 2by = 0
m) pass through the origin and cuts off intercept equal to 3, 4 from x-axis. x² + y² - 3x - 4y = 0
n) pass through the origin and cuts off intercept equal to 2a, 2b from y-axis. x² + y² - 2ax - 2by = 0
o) touch the axis of x at a distance of 4 from the origin and cut off an intercept of 6 from the axis of y. x² + y² ± 8x ± 10y +16 = 0
p) centre in the first quadrant touches the y-axis at the point (0,2) and passes through the point (1,0). Find the equation of the circle. x² + y² - 5x - 4y +4 = 0
q) centre (1,0), which passes through the point (3, 3/2). Find also the equation of the equation which touches the given circle externally at P. 4x² + 4y² - 8x - 21 = 0, 4x² + 4y² - 40x - 24y +111 = 0
10) Find the equation of the circle whose centre is (3, -1) and which cut-off an intercept of length 6 from the line 2x - 5y +18= 0. x² + y² - 6x + 2y - 28 = 0
11) If the line 2x - y +1 = 0 touches the circle at the point (2,5) and the centres of the circle lies on the line x+ y - 9 = 0. Find the equation of the circle. (x - 6)² + (y - 3)² = 20
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