1.

Find equation of circle concentric with the circle x2 + y2 - 2x - 4y - 5 = 0 and area is double 1. x2 + y2 - 3x - 4y - 10 = 02. x2 + y2 - 2x - 4y - 15 = 03. x2 + y2 - 2x - 4y - 10 = 04. x2 + y2 - 3x - 4y - 15 = 0

Answer» 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.


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