Does the point (-10,3) lie on the circle that passes through the point (-2,9) with center (-3,2)? explain

yes

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 3, 2), so

(x + 3)² + (y - 2)² = r²

r is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (- 2, 9)

r = = = , hence

(x + 3)² + (y - 2)² = 50 ← equation of circle

Substitute (- 10, 3) into the left side of the equation and if equal to the right side then the point lies on the circle

(- 10, 3) : (- 10 + 3)² + (3 - 2)² = (- 7)² + 1² = 49 + 1 = 50

Hence (- 10, 3) lies on the circle

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.