find the values of p so that the equation x^2 + y^2 - 2px +4y - 12 = 0 may represent a circle of radius 5 units
We know that x²+y² +2gx + 2fx + c= 0 always represent a Circle where center of circle is C( -g, -f ) and Radius of circle => R² = g² + f² - c
Now, for Equation : x²+y²-2px+4y-12=0
Comparing this equation with general formula, we get,
2g = 2p
Thus, g = p
and 2f = 4
Thus f= 2
Thus g=p and f=2
Now Radius given = 5 units
Thus,
R² = g² + f² - c
(5)² = p² + (2)² -12
25 = p² + 4-12
25 = p² - 8
p² = 33
p = √33
Now, for Equation : x²+y²-2px+4y-12=0
Comparing this equation with general formula, we get,
2g = 2p
Thus, g = p
and 2f = 4
Thus f= 2
Thus g=p and f=2
Now Radius given = 5 units
Thus,
R² = g² + f² - c
(5)² = p² + (2)² -12
25 = p² + 4-12
25 = p² - 8
p² = 33
p = √33