Question

The equation of circle passing through (4, 5) and having the centre at (2, 2), is

Answer 1

x² + y² - 4x - 4y - 5 = 0

Solution:

The coordinates of the center of the circle is (2, 2). A point on the circle is given by the coordinates (4, 5).

By these two, we can find the length of the radius of the circle by distance formula.

    √[(4 - 2)² + (5 - 2)²]

⇒  √(2² + 3²)

⇒  √(4 + 9)

⇒  √13

Hence the radius is √13 units long.

Let there be a point (x, y) on the circle.

With this point (x, y) and the center (2, 2), we can write the radius as,

    √[(x - 2)² + (y - 2)²] = √13

⇒  (x - 2)² + (y - 2)² = 13

⇒  x² - 4x + 4 + y² - 4y + 4 = 13

⇒  x² + y² - 4x - 4y + 8 = 13

⇒  x² + y² - 4x - 4y + 8 - 13 = 0

⇒  x² + y² - 4x - 4y - 5 = 0

Thus we derive the equation of the circle.

Answer 2

Answer:

x^2+y^2-4x-4y-5 = 0.....