Definition of a circle

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Question

The greatest distance of the point $P (10, 7)$ from the
circle $x^{2} + y^{2} - 4 x - 2 y - 20 = 0$ , is

Moderate

Solution

We have,
$S_{1} = 10^{2} + 7^{2} - 4 \times 10 - 2 \times 7 - 20 > 0$
So, $P$ lies outside the circle.
Join $P$ with the centre $C (2, 1)$ of the given circle. Suppose $P C$
cuts the circle at $A$ and $B .$ Then, $P B$ is the greatest distance of $P$
from the circle.
Now, we have
$P C = \sqrt{(10 - 2)^{2} + (7 - 1)^{2}} = 10$
and, $C B = R a d i u s$ $= \sqrt{4 + 1 + 20} = 5$
$∴ P B = P C + C B = (10 + 5) = 15$

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Definition of a circle

Remember concepts with our Masterclasses.

The greatest distance of the point P (10, 7) from the circle x2+y2−4x−2y−20=0, is

Ready to Test Your Skills?

free study material

The greatest distance of the point $P (10, 7)$ from the
circle $x^{2} + y^{2} - 4 x - 2 y - 20 = 0$ , is