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Find the equation of the normals to the ...

Find the equation of the normals to the circle `x^2+y^2-8x-2y+12=0` at the point whose ordinate is `-1`

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We have circle `x^(2)+y^(2)-8x-2y+12=0`
Centre of the circle is C(4,1).
Putting `y= -1` in the equation of the circle, we get
`x^(2)-8x+15=0`
`implies(x-3)(x-5)=0`
`implies x=5 ` or 3
Thus, the points on the circle are P(5,-1) and Q(3,-1).
Equation of normal at P is
`y+1=(-1-1)/(5-4)(x-5)`
or `2x+y-9=0`
Equation of normal at Q is
`y+1=(-1-1)/(3-4)(x-5)`
or `2x-y-7=0`
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