Question

The equation of a circle is x2+y2+4x-2y-20=0 . Atangentisdrawn from the point (5,2) to this circle. Find the distance from the point of contact to the point (5,2).

Answer 1

Hi,

Answer: 5

Explanation:

We find first the center of the circle:

`x^2+y^2+4x-2y-20=0\\x^2+4x+4+y^2-2y+1-25=0\\\\(x+2)^2+(y-1)^2=5^2\\\\center=(-2,1)\\radius=5\\`

We find distance(P,C):

PC²=(5-(-2))²+(2-1)²=49+1=50

Distance(BC): the radius

BC²=25

Using the Pythagorean's theorem:

PB²=PC²-BC²=50-25=25

|PB|=5