Question

If a circle c whose radius is 3 touches externally the circle

Answer 1

The options for this question are missing. Here are the missing options:

a) 2√5

b) 3√2

c) √5

d) 2√3

The correct answer for this question is option a) 2√5

If there is any confusion please leave a comment below.

Answer 2

Answer:

2√5

Step-by-step explanation:

Hi,

Let the center of the circle c be 'A

Given radius of the circle c as 3,

Also, given that the circle c touches x² + y² + 2x - 4y - 4 = 0 at point D(2, 2).

Center of the given circle is B (-1, 2) and the radius of the given circle is

√1² + 2² + 4 = 3.

Since 2 circles touch each other externally at D(2, 2) , center A , D and B lie

on a straight line.

But equation of line BD is y = 2 since both the points B and D have same y-

coordinate as 2.

Thus,  center of circle c will also have y-coordinate 2.

Now, since circles touch each other externally, distance between center's

should be equal to sum of their radii,

hence A will have its coordinates as (5, 2).

Hence the equation of circle c will be

(x - 5)² + (y - 2)² = 3²

Now to find the intercept of circle on x- axis , let y = 0

⇒ (x - 5)² + 4 = 9

⇒ (x - 5)² = 5

⇒ x - 5 = ±√5

⇒ x = 5 ± √5

Let x₁ = 5 + √5 and x₂ = 5 - √5

Hence , the x-intercept will be x₁ - x₂ = 2√5

Hope, it helped !