Question

Find equation of circle concentric with the circle x² + y² - 2x - 4y - 5 = 0 and area is double 

1. x² + y² - 3x - 4y - 10 = 0
2. x² + y² - 2x - 4y - 15 = 0
3. x² + y² - 2x - 4y - 10 = 0
4. x² + y² - 3x - 4y - 15 = 0

Answer 1

Correct Answer - Option 2 : x² + y² - 2x - 4y - 15 = 0

Concept:

The center of the circle x2 + y2 + 2gx + 2fy + c = 0 is (-g, -f) and its radius r is given by r2 = g2 + f2 - c.

 

Calculation:

The given equation of the circle is x2 + y2 - 2x - 4y - 5 = 0.

Comparing it with the general equation of the circle we get:

g = -1, f = -2, c = -5

Using the relation r2 = g2 + f2 - c, we get:

⇒ r2 = (-1)2 + (-2)2 - (-5)

⇒ r = √10

For doubling the area, the radius must become √2 times.

∴ Required radius = √20.

Center is (-g, -f) = (1, 2).

Equation of the circle is: (x - 1)² + (y - 2)² = (√20)²

⇒ x² + y² - 2x - 4y - 15 = 0.