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Question

Find the area of the triangle formed by the normal at (3,4) to the circle x2+y222x4y+25=0 with the coordinate axes.

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Solution

Normal of a circle at given point (x1,y1)=yy1=y1+fx1+g(xx1)

here g=11,f=2

equation of normal :y(4)=4+2211(x3)

y+4=29(x3)

9y+36=2x6

2x9y42=0

X-intercept of given normal=422=21
Y-intercept of given normal=429=143

Area=12×21×143=49 cm2

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