Question

13. What is the equation of a circle with center (8,4) and radius 7?(x - 8)2 + (y - 4)2 = 7(x - 8)2 + (y - 4)2 = 49(X + 8)2 + (y + 4)2 = 7(X + 8)2 + (y + 4)2 = 49

Answer 1

Step 1: Write out the formular for the equation of a circle with the radius and the centre of the circle given.

(x-a)² + (y-b)² = r²

Step 2: Write out the given data

a= 8

b=4

r= radius= 7

Step 3: Substituting the values

`\begin{gathered} (x-8)^2+(y-4)^2=7^2 \\ (x-8)(x-8)+(y-4)(y-4)=49 \\ x(x-8)-8(x-8)+y(y-4)-4(y-4)=49 \end{gathered}`
`\begin{gathered} x^2-8x-8x+64+y^2-4y-4y+16=49 \\ x^2-16x+64+y^2-8y+16=49 \\ \text{Collecting like terms and rearranging} \\ x^2+y^2-16x-8y+64+16-49=0 \\ x^2+y^2-16x-8y+31=0 \end{gathered}`

Hence the equation of the circle is x²+y²-16x-8y+31=0.