Homework

Problem 1 · easy

Write the equation of the circle with center (0,0) and radius 7.

Problem 2 · easy

Write the equation of the circle with center (3,-2) and radius 5.

Problem 3 · easy

Find the center and radius of (x+4)^2 + (y-1)^2 = 36.

Problem 4 · medium

Convert to standard form and find center/radius: x^2 + y^2 - 6x + 2y - 6 = 0.

Problem 5 · medium

Convert: x^2 + y^2 + 8x - 4y - 5 = 0.

Problem 6 · easy

Complete the square for x^2 + 10x.

Problem 7 · medium

For x^2 = 12y, find the focus and directrix.

Problem 8 · medium

For y^2 = -8x, find the focus, directrix, and opening direction.

Problem 9 · medium

Write the equation of the parabola with vertex (0,0) and focus (0,4).

Problem 10 · medium

Write the equation of the parabola with vertex (0,0) and focus (3,0).

Problem 11 · easy

Find the vertex of f(x) = -(x-2)^2 + 7.

Problem 12 · medium

Convert to vertex form: f(x) = x^2 + 4x - 1.

Problem 13 · easy

For f(x) = 3(x-1)^2 + 2, state vertex, axis of symmetry, and direction.

Problem 14 · medium

Write the equation of the parabola with vertex (2,-3) and passing through (4,1).

Problem 15 · medium

A parabola has vertex (-1,4) and opens downward with a=2. Write its equation.

Problem 16 · medium

Find the focus of y = x^2 (vertex at origin, a=1).

Problem 17 · challenge

Does x^2 + y^2 + 2x + 2y + 3 = 0 represent a circle? Why or why not?

Problem 18 · medium

Find the equation of the circle that passes through (0,0), center at (3,4).

Problem 19 · medium

A satellite dish has parabolic cross-section modeled by x^2 = 8y. How deep is the dish at x=4?

Problem 20 · easy

Find the y-intercepts of the circle x^2 + y^2 = 25.

Problem 21 · medium

Find the x-intercepts of (x-3)^2 + y^2 = 16.

Problem 22 · challenge

Convert to vertex form: f(x) = 2x^2 + 12x + 11.

Problem 23 · medium

Write the equation of the circle with diameter from (-1,2) to (5,2).

Problem 24 · medium

For y^2 = 20x, find the focus and directrix.

Problem 25 · challenge

A parabola has focus (0,2) and directrix y=-2. Write its equation.