Question

Find the equation of the circle whose centre is (3, -2) and which cuts off an intercept of length 6 on the line 4x - 3y + 2 =0

Answer 1

Answer:

Ggle

Step-by-step explanation:

Mark meBrainliest and follow

Answer 2

Step-by-step explanation:

(x - 3)² + (y + 2)² = 25 (Standard form).

x² - 6x + y² + 4y - 12 = 0 (General form

Main idea

The radius is a perpendicular bisector to the chord. (Picture attached.)

Explanation

The pieces of information about the circle

are

1. Its center is (3,-2).

2.4x3y + 2 = 0 cuts through the circle

We should obtain the distance of (3,-2) to the line 4x - 3y + 2 = 0 from the distance formula,

d ax₁ +by₁ + c √a² +6² -

Now we get,

→ d 12+ 6+2 4² +32

20 5 → d -

d = 4.There forms a right triangle that consists of the equally divided chord, radius, and perpendicular line.

Let's solve for the radius r.

p² = 3² +4²

⇒ r = 5.

Hence,

r = 5.

And hence, the equation of the circle is,

(x-3)² + (y + 2)² = 25.