已知方程x2+y2-2(t+3)s+2(1-4t2)y+16t4+9=0,其求中面积最大的圆的方程
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![已知方程x2+y2-2(t+3)s+2(1-4t2)y+16t4+9=0,其求中面积最大的圆的方程](/uploads/image/z/1270612-28-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8Bx2%2By2-2%28t%2B3%29s%2B2%281-4t2%29y%2B16t4%2B9%3D0%2C%E5%85%B6%E6%B1%82%E4%B8%AD%E9%9D%A2%E7%A7%AF%E6%9C%80%E5%A4%A7%E7%9A%84%E5%9C%86%E7%9A%84%E6%96%B9%E7%A8%8B)
已知方程x2+y2-2(t+3)s+2(1-4t2)y+16t4+9=0,其求中面积最大的圆的方程
已知方程x2+y2-2(t+3)s+2(1-4t2)y+16t4+9=0,其求中面积最大的圆的方程
已知方程x2+y2-2(t+3)s+2(1-4t2)y+16t4+9=0,其求中面积最大的圆的方程
对方程进行化简
x^2+y^2-2(t+3)x+2(1-4t^2)y+16^4+9=0
[x^2-2(t+3)x+(t+3)^2]+[y^2+2(1-4t^2)y+(1-4t^2)^2]+[-(t+3)^2-(1-4t^2)^2+16t^4+9]=0
[x-(t+3)]^2+[y+(1-4t^2)]^2+[-t^2-6t-9-1-16t^4+8t^2+16t^4+9]=0
[x-(t+3)]^2+[y+(1-4t^2)]^2+[-6t-1+7t^2]=0
化简得
[x-(t+3)]^2+[y+(1-4t^2)]^2=-7t^2+6t+1=-7(t^2-6t/7+9/49)+9/7
[x-(t+3)]^2+[y+(1-4t^2)]^2=-7(t-3/7)^2+9/7
当圆面积最大时,t=3/7,半径为R=3/(根号7)
此时圆的方程为(x-24/7)^2+(y+13/49)^2=9/7
圆的最大面积为S=πR^2=9π/7