PUPIENUNCI Find the shortest and la...
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PUPIENUNCI Find the shortest and largest distance from the point (2, - 7) to the circle x2 + y2 - 14x - 10y - 151 = 0

JEE/Engineering Exams
Maths
Solution
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Let ( S=x^{2}+y^{2}-14 x-10 y-151=0 ) Substituting the point (2,-7) in this equation, we get ( S_{1}=(2)^{2}+(-7)^{2}-14(2)-10(-7) ) ( -151=-56<0 ) ( therefore P(2,-7) ) inside the circle Radius of circle ( r=sqrt{(-7)^{2}+(-5)^{2}+151}=15 ) Centre of circle (7,5) ( mathrm{CP}=sqrt{(7-2)+(5+7)^{2}}=13 ) Shortest distance ( = ) ( P A=r-C P=15-13=2 ) Largest distance ( P B=r+C P=15+13=28 )
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