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A circle is centered at H (4,0) and has a radius of 10. Where does the point L(-2,8) lie? (khan)

a. inside the circle
b. on the circle
c. outside the circle

1 Answer

7 votes

Answer:

b) on the circle

The point lies on the circle S =0

Explanation:

Step(i):-

Given center of the circle = H(4,0)

Radius of the circle 'r' = 10

Equation of the circle


(x -h)^(2) +(y-k)^(2) = r^(2)


(x -4)^(2) +(y-0)^(2) = 10^(2)


(x )^(2) -8 x + 16 + (y)^(2) = 10^(2)


(x )^(2) -8 x + (y)^(2) = 10^(2) - 16


x ^(2) -8 x + y^(2) = 84

Step(ii):-

S =0 is a circle and P(x₁ , y₁) be a point in its plane

Then (i) P lies inside the circle S = 0 ⇔ S₁₁ < 0

ii) P lies outside the circle S = 0 ⇔ S₁₁ > 0

iii) P lies on the circle S = 0 ⇔ S₁₁ = 0

now


S_(11) = x^(2) _(1) + y^(2) _(1) + 2 g x_(1) + 2 f y_(1) +c


S_(11) = x_(1) ^(2) -8 x_(1) + y_(1) ^(2) = 84

Given point ( -2 , 8)


S_(11) = (-2) ^(2) -8 (-2) + (8) ^(2) -84 = 0

P lies on the circle S = 0 ⇔ S₁₁ = 0

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