What is power?

Geometry Level 3

Power of a point (2,5) is negative with respect to circle

$x^{2} + y^{2} -8x -12y + P = 0$

And circle neither touches nor intersect both coordinate axis.

The range value of P can be wriiten as a < P < b

Then find

a + b

The answer is 83.

1 solution

Krishna Sharma
Sep 27, 2014

Power of point is negative which means point is inside circle Put the point in circle Which will be less than zero $2^{2} + 5^{2} -8 \times 2 - 12 \times 5 + P < 0$ Which gives P < 47

Circles neither touches nor intersect coordinate axis Hence

$g^{2} < c$ (intercept made by circle on x-axis)

Gives $P > 16$

And

$f^{2} < c$ (intercept made by circle on y-axis)

Gives $P > 36$

Therefore, $36<P<47$ So the answer is $\boxed {83}$

What is power?

The answer is 83.

1 solution

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