Question

18) If the straight line y=m X touches the circle (x - 2)^2 + (y - 6)^2 = 4, then m= ......

(a)1/3. (b)2/3. (c)-4/3. (d)4/3
(19) ABCD is a rectangle in which A=(-1,4), B = (1,8),C=(9,4), D=(1,0)
then the equation of the circumcircle of the rectangle is.......
(21)
(a) (X - 4)^2 + (y-4)^2= 25
(b)(x-4)^2 + (y - 4)^2 = 16
(c) (x + 4)^2 + (y + 4)^2 = 25 (d) (x – 4)² + (y + 4)² = 16​

Answer 1

(8) d. 4/3 (9) a. (X - 4)^2 + (y-4)^2= 25

Explanation:

8. CENTER OF CIRCLE: O (2,6)

radius of circle : r = √4 = 2

if m = 4/3 line: y = 4/3 x

perpendicular distance (d) from center of circle to line y = 4/3 x is

d = |((4/3 x 2) + (-1) x 6)| / √((4/3)² + (-1)²) = |(-10/3)| / √(25/9) = (10/3) / (5/3) = 2

d = r means line touch with circle

9. center of circle is the intersection of the diagonals of rectangle (4,4) and its radius is 5 (illustrated)

the equation of circle: (X - 4)^2 + (y-4)^2= 25