Question

Radius of the circle (x - 1)(x - 3) +(y-2)(y-4) = 0 is
(a) 2
(b) 2
(d) 2√2
(C) 3​

Answer 1

Answer:

√2

Step-by-step explanation:

Just simplify the above equation and then compare it with general equation of circle.

Then apply formula of finding radius √g^2 + f^2+c and you will get the answer.

Answer 2

Given:

The equation of a circle is (x-1)(x-3) + (y-2)(y-4) = 0.

To Find:

The radius of the given circle.

Solution:

The given problem can be solved by using the concepts of circles.

1. Consider a circle with radius r. Let the coordinates of the circle of the two opposite sides of the circle (x1, y1) and (x2, y2).

2. The distance between the two points above is known as the diameter. The radius of the circle is half the length of its diameter.

3. Therefore diameter =$\sqrt{({x1-x2})^2 +(y1-y2)^{2} }$,

4. The equation of a circle with endpoints of the diameter as (x1, y1) and (x2, y2) is (x-x1)(x-x2)+ (y-y1)(y-y2) = 0,

=>Values of x1, y1, x2, y2 is 1, 3, 2, 4 respectively.

5. Therefore,the diameter of the given circle is,

=> Diameter =$\sqrt{2^{2} +2^{2} }$,

=> Diameter = 2√2.

6. Therefore, the radius of the given circle is ( 2√2/2) = √2 units.

Therefore, the radius of the circle is √2 units. Option B is the correct answer.