Hello. I’m new here and I need help with my math homework. Please help me as soon as possible because I am confused and stressed.

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

1) You need to figure out the distance of each point from (4,-3). Got a circle compass? Put the point at (4,-3) and open it up 5 units, measuring along the grid. Now draw a circle around (4,-3). Points on or within the circle are within 5 units. Points outside the circle are not.

Don't have a compass? Compute the distance to each point (x,y) from (4,-3) as follows:

(x-4)² + (y+3)²

If that sum is less than equal to 25, the point is within 5 units of (4,3); otherwise it is not.

2) Choices C) and D) are not ellipses - they are hyperbolas. Choices A) and B) are ellipses. A) has the major axis aligned along the y-axis, b) has the major axis aligned along the x-axis. The vertex is at (0,11) and the co-vertex is at (4,0); so the major axis is along the y-axis. A) is the answer.