Question

The value of p, for which the equation x² + y² - 2px + 6y - 7 = 0 represents a circle of radius 5 units, is:

1. ±4
2. ±3
3. ±2
4. ±1

Answer 1

Correct Answer - Option 2 : ±3

Concept:

The radius of the circle x² + y² + 2gx + 2fy + c = 0 is given by r² = g² + f² - c.

 

Calculation:

Comparing the given equation x2 + y2 - 2px + 6y - 7 = 0 with the general equation of the circle we get:

g = -p, f = 3, c = -7

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

⇒ 52 = (-p)2 + 32 - (-7)

⇒ 25 = p2 + 9 + 7

⇒ p² = 9

⇒ p = ±3