Question

Please help me..

In the figure, the circle A with x passes through the centre y of the circle B is x^2+ y^2-4x+6y-12=0 and coordinates of x are (-4,5) then find the equation of circle A.​

Answer 1

Answer: A: (x + 4)² + (y - 5)² = 8

Explanation:

The equation of a circle is: (x - h)² + (y - k)² = r² where

• (h, k) is the center of the circle
• r is the radius of the circle

To find the equation of circle A, we need (h, k) and r².

It is given that (h, k) = (-4, 5)

The distance between the center of circles A and B is the radius of circle A.

Let's find the center of circle B by completing the square:

x² - 4x + ____ + y² + 6y + _____ = 12 + ____ + _____

↓ ↓

h = -4/2 k = 6/2

h = -2 k = 3 → Circle B has center (-2, 3)

Now let's find the distance between the center of circles A and B:

`(r_A)^2=d^2=(x_A-x_B)^2+(y_A-y_B)^2`

= (-4 - (-2))² + (5 - 3)²

= (-2)² + 2²

= 4 + 4

= 8

Now we have the the center (h, k) and the r² for circle A:

(h, k) = (-4, 5) and r² = 8 → (x + 4)² + (y - 5)² = 8