Question

Find the largest and the shortest distance from the point 2, - 7 to the circle

Answer 1

Answer:

(a)2and28(b)4and20(c)3and27(d)5and25

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A)

Let S=x2+y2−14x−10y−151=0

Substituting the point (2,−7) in this equation, we get

S1=(2)2+(−7)2−14(2)−10(−7)−151=−56<0

∴P(2,−7) inside the circle

Radius of circle r=(−7)2+(−5)2+151−−−−−−−−−−−−−−−−√=15

Centre of circle (7,5)

CP=(7−2)+(5+7)2−−−−−−−−−−−−−−√=13

Shortest distance =PA=r−CP=15−13=2

Largest distance PB=r+CP=15+13=28

Hence (a) is the correct answer