Question

find the eqn of circle with centre c and radius r where c=(-1/2,-9) r=5 sol: 4x^2+4y^2+4x+72y+225=0​

Answer 1

Answer:

we know , equation of circle:

(x-h)²+(y-k)² = r² where (h,k) is the centre and r is radius.

$acc \: to \: ques \\ (h,k) = ( \frac{ - 1}{2} ,9) \: and \: r \: = 5 \\ eqn = > {(x - \frac{ - 1}{2}) }^{2} + {(y - ( - 9))}^{2} = {5}^{2} \\ = > {( \frac{(2x + 1)}{2} )}^{2} + {(y + 9) }^{2} = 25 \\ = > \frac{{(2x + 1)}^{2} }{4} + {(y}^{2} + 18y + 81) = 25 \\ = > (4 {x}^{2} + 4x + 1) + 4( {y}^{2} + 18y + 81) = 25 \times 4 \\ = > 4 {x}^{2} + 4x + 1 + 4 {y}^{2} + 72y + 324 = 100 \\ = > 4 {x}^{2} + 4 {y}^{2} + 4x + 72y + 325 - 100 = 0\\ = > 4 {x}^{2} + 4 {y}^{2} + 4x + 72y + 225 = 0$