Questions & Answers

Question

Answers

A. 25

B. 24

C. 36

D. 38

Answer

Verified

128.4k+ views

As we know that the power of any point with respect to any conic is negative when the point is inside that conic and positive when the point is outside that conic. And the power of point is equal to zero when the point lies on the conic.

And to find the power of a point with respect to any conic (here circle) we had to put the coordinates of that point in the equation of conic.

So, here to find the power of point (0, 0) with respect to the given circle \[{x^2} + {y^2} + 2x + 4y + 25 = 0\]. We had to substitute the value of x = 0 and y = 0 in the equation of the circle.

So, the power of point (0, 0) will be \[{\left( 0 \right)^2} + {\left( 0 \right)^2} + 2\left( 0 \right) + 4\left( 0 \right) + 25 = 25\]

Hence, the power of the origin (i.e. (0, 0) with respect to the circle \[{x^2} + {y^2} + 2x + 4y + 25 = 0\] will be 25.