Find the equation of a tangent to the circle
x^2+y^2+gx + fy=0 at (-g; -f).
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Answer:
Step-by-step explanation:
Referring to the figure:
OA=OC (Radii of circle)
Now OB=OC+BC
∴OB>OC (OC being radius and B any point on tangent)
⇒OA<OB
B is an arbitrary point on the tangent.
Thus, OA is shorter than any other line segment joining O to any
point on tangent.
Shortest distance of a point from a given line is the perpendicular distance from that line.
Hence, the tangent at any point of circle is perpendicular to the radius.
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