Question

Find the equation of the circle which passes through (2,3) , having its centre on x

axis and radius 5 units.​

Answer 1

Given ,

The circle passes through (2,3) having its centre on x axis and radius 5 units

We know that , the equation of circle is given by

$\tt {(r)}^{2} = {(x - h)}^{2} + {(y - k)}^{2}$

Where ,

Coordinate of circle = (h , k)

Thus ,

(5)² = (2 - h)² + (3 - 0)²

25 = (2)² + h² - 2 × 2 × h + 9

25 = 4 + h² - 4h + 9

25 = h² - 4h + 13

h² - 4h - 12 = 0

h² - 6h + 2h - 12 = 0

h(h - 6) + 2(h - 6) = 0

(h + 2)(h - 6) = 0

h = -2 or h = 6

When , h = -2

The equation of circle :

(5)² = (x + 2)² + (y)²

25 = x² + (2)² + 2 × 2 × x + y²

25 = x² + 4 + 4x + y²

25 = x² + y² + 4x + 4

x² + y² + 4x - 21 = 0

When , h = 6

The equation of circle :

(5)² = (x - 6)² + (y)²

25 = x² + (6)² - 2 × 6 × x + y²

25 = x² + 36 - 12x + y²

25 = x¹ + y² - 12x + 36

x² + y² - 12x + 11 = 0

Therefore , the equation of circle is x² + y² + 4x - 21 = 0 or x² + y² - 12x + 11 = 0

____________ Keep Smiling ☺