Please help me with my Algebra homework I need help as soon as possible please please

Question

1.) Which points on the graph shown are within 5 units of the point (4, −3)?

   A.) P, Q, R

   B.) N, O, P

   C.) R, S, T

   D.) L, M, N

2.) Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (0, 11), and a co-vertex at (4, 0).

A.)

B.)

C.)

D.)

Answer 1

The set of points that lie 5 units from the point (4,-3) is the circle with center (4,-3) and radius 5.

An equation for that circle is (x-4)² + (y+3)² = 25

On graph paper, carefully plot the points and then draw the circle (preferably with a compass) to see which of the points are inside the circle. I think the answer is choice A, but double check with the graph. .

For the second problem, the points (0,11) and (4,0) satisfy only equation A, so that's the one.