Question

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

Answer 1

Point L(-2, 8) lies on the circle centered at H(4, 0) with a radius of 10, as it is exactly 10 units away from H.

Step-by-step explanation:

The question concerns the location of a point L(-2, 8) in relation to a circle with a center at H(4, 0) and a radius of 10. To determine whether point L lies inside, on, or outside the circle, we need to calculate the distance between point H and L and compare it with the radius of the circle.

Let's calculate the distance (d) using the distance formula: d = √((x2-x1)2 + (y2-y1)2). Plugging in the values, we get d = √((-2-4)2 + (8-0)2) = √(36 + 64) = √100 = 10. Since this distance is equal to the radius of the circle, point L lies on the circle.

Answer 2

Step-by-step explanation:

HL=√((-2-4)²+(8-0)²)=√(36+64)=√100=10=radius

so L lies on the circumference of circle.

or eq. of circle is (x-4)²+(y-0)²=10²

(x-4)²+y²=100

Put x=-2,y=8

(-2-4)²+8²=100

36+64=100

or 100=100

which is true.

Hence L lies on the circle.