# math question

• Oct 31st 2007, 07:15 AM
pramod khanal
math question
find the equation of circle which passes through the point(4,1)and(6,5)and whose center lies on the line 4x+y=16
• Oct 31st 2007, 07:32 AM
Krizalid
Principal equation of circle states that

\$\displaystyle (x-h)^2+(y-k)^2=r^2,\$ where \$\displaystyle (h,k)\$ & \$\displaystyle r\$ are its center and radius respectively.

Since points \$\displaystyle (4,1)\$ & \$\displaystyle (6,5)\$ satisfy the equation, plug'em into the aforesaid equation.

Besides, its center lies on the line \$\displaystyle 4x+y=16,\$ so \$\displaystyle 4h+k=16.\$

You need to solve a system of equations.
• Oct 31st 2007, 09:41 AM
earboth
Quote:

Originally Posted by pramod khanal
find the equation of circle which passes through the point(4,1)and(6,5)and whose center lies on the line 4x+y=16

Hello,

Krizalid has given all necessary equations to calculate the coordinates of the centre of the circle and the length of the radius.
I've attached a construction so you have the possibility to check your answers.