Question

Find the equation of the circle with centre
() At (a, b) touching the Y-axis
(ii) At (-2, 3) touching the X-axis
(ii) on the X-axis and passing through the
origin having radius 4.
(iv) at (3,1) and touching the line
8x – 15y + 25 = 0
​

Answer 1

x² + y²  - 2ax - 2by + b² = 0 , x² + y² + 4x - 6y + 4 = 0 and x² + y² ± 8x = 0

Step-by-step explanation:

equation of the circle with center  At (a, b) touching the Y-axis

Touching y axis  => radius = a

(x - a)² + (y - b)² = a²

=> x² + a² - 2ax + y² + b² - 2by = a²

=> x² + y²  - 2ax - 2by + b² = 0

At (-2, 3) touching the X-axis => Radius = 3

(x + 2)² + (y - 3)² = 3²

=> x² + 4 + 4x + y² + 9 - 6y = 9

=> x² + y² + 4x - 6y + 4 = 0

on the X-axis and passing through the origin having radius 4

=> (x  ± 4)²  + y² = 4²

=> x²  + 16 ± 8x + y² = 16

=> x² + y² ± 8x = 0

Learn more:

find the equation of circle which passed through origin and cuts off ...

https://brainly.in/question/2075668

equation of circle touching x axis at origin and the line 4x -3y +24=0 ...

https://brainly.in/question/8752653

Answer 2

I hope it's very useful for us