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Sedaia [141]
2 years ago
7

If the radius of the circle x² + y2 - 4x - 6y - k = 0 is4 units, find the value of k.​

Mathematics
1 answer:
meriva2 years ago
5 0

Answer: 3

Step-by-step explanation:

Given

The equation of the circle is x^2+y^2-4x-6y-k=0

Using completing the square method

\Rightarrow x^2+y^2-4x-6y+4-4+9-9-k=0\\\Rightarrow \left( x^2-4x+4\right)+\left( y^2-6y+9\right)-\left( k+4+9\right)=0\\\Rightarrow \left( x-2\right)^2+\left( y-3\right)^2=\left( k+13\right)

on comparing with standard form,  r^2=k+13

Insert the value of r

\Rightarrow 4^2=k+13\\\Rightarrow k=16-13\\\Rightarrow k=3

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Line segment ON is perpendicular to line segment ML, and PN = 10.
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we know that

Triangle MOL is an isosceles triangle

because

MO=OL=radius\ of\ circle=25\ units

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