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Question

Show that the line 7yx=5 touches the circles x2+y25x+5y=0 and find the equation of the other parallel tangent.

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Solution

x2+y25x+5y=0
centre of circle is C(52,52)
Radius of circle =(52)2+(52)20=522
Let the perendicular distance of line from centre =p
7yx=5x7y+5=0
p=527(52)+51+49=522p=r
So the given line is tangent to circle
Slope of given line =17
So by using equation of tangent in slope form , equations of tangents are
y=17x±5221+149y=x±2577y=x+257yx=25

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