Question

Find the values of p so that x2+y2+8x+10y+p=0 is the equation of a circle of radius 7 units

Answer 1

Answer:

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Answer 2

given an equation of circle of radius $7$ units, find the value of 'p'

Explanation:

1. equation of a circle having co- ordinates of center (h, k) and radius 'r' is given by,     $(x-h)^2+(y-k)^2=r^2$    
2. expanding the above equation we get, $x^2+y^2-2hx-2ky+(h^2+k^2-r^2)=0$   ----(a)  
3. given equation of circle is,  $x^2+y^2+8x+10y+p=0$    ----(b)
4. comparing (a) and (b) we get, $h=-4\ and\ k=-5$  
5. hence since radius of given circle is $7$ units we get,                                              $p=h^2+k^2-r^2 \\p=(-4)^2+(-5)^2-7^2 = 16+25-49\\p=-8$  -------->ANSWER