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Question

The point (x1,y1) lies inside the circle x2+y2+2gx+2fy+c=0, if x21+y21+2gx1+2fg1+c is less than zero


A

True

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B

False

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Solution

The correct option is A

True


From the figure we can see that, PC<r. this is the condition for P to lie inside the circle.

The coordinates of P are (x1,y1) and

C(g,f)

r=g2+f2c

PC<r

(x1+g)2+(y1+f)2<g2+f2c

x21+y21+2gx1+2fy1+c<0

The given statement is correct


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