Question 984216
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{{{x^2+y^2-6x+8y-24=0}}}
{{{(x^2-6x)+(y^2+8y)=24}}}Complete the squares
{{{(x^2-6x+9)+(y^2+8y+16)=24+9+16}}}
{{{(x-3)^2+(y+4)^2=7^2}}}
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Standard form for circle:
{{{(x-h)^2+(y-k)^2=r^2}}}
Where (h,k) is center of circle and r=radius.
So the center of our circle is at (3,-4) with radius=7.
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The equation of the diameter will be the equation through the center and the given point:
Find the line through (-1,1) and (3,-4) 
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Find the slope:
m=(change in y)/(change in x)=(1-(-4))/(-1-3)=(5/-4)=-(5/4)
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In slope intercept form:
y=mx+b
y=-(5/4)x+b Put in values of the given point and solve for b.
1=-(5/4)(-1)+b
4/4=5/4+b
-1/4=b
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Write the final equation:
y=-(5/4)x-1/4