Question

21. The centre of a circle with radius 5 is (2,3)
(a) What is the equation of the circle ?
(b) What are the coordinates of point where the circle cut x axis?
(c) Write the coordinates of another point on the circle.​

Answer 1

Answer:

(a)  ( x - 2 )² + ( y - 3 )² = 25

(b)  (-2, 0) and (6, 0)

(c)  (5, 7)

Step-by-step explanation:

(a) The equation of a circle with centre (a, b) and radius r is

         ( x - a )² + ( y - b )² = r².

So the equation of the circle with centre (2, 3) and radius 5 is

        ( x - 2 )² + ( y - 3 )² = 25.

(b)  A point (x, 0) on the x-axis is also on the circle if it satisfies the equation of the circle.  So we put (x, 0)  [ i.e. y = 0 ] into the equation and solve for x:

       ( x - 2 )² + ( 0 - 3 )² = 25

 ⇒  ( x - 2 )² + 9 = 25

 ⇒  ( x - 2 )² = 25 - 9 = 16

 ⇒    x - 2  =  ±4

 ⇒   x = 2 ± 4 = -2 or 6.

So the circle cuts the x-axis at the two points (-2, 0) and (6, 0).

(c)  Since 3² + 4² = 25, we can find points that satisfy the equation of the circle if we make x-2 = 3 and y-3=4.

So the point (x, y) = (5, 7) is on the circle.

Hope this helps!