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Grade 11 · unit review

Review: Algebra2: Conic Equations and Features

Circle, parabola, ellipse and hyperbola equations encode geometric features through squared quantities and sign patterns. Standard forms locate centers, focal information, axes or vertices, with care to distinguish full lengths from half lengths.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Identify center and radius of (x−7)²+(y+8)²=49.
Need a hint?
  • The squared-distance circle form (x−h)²+(y−k)²=r² encodes a center and nonnegative radius.
  • The signs in the differences are opposite the center’s coordinate signs.
2. For x²=28y, find the focus.
Need a hint?
  • The vertical parabola x²=4py consists of points equally distant from focus (0,p) and directrix y=−p.
  • Divide the y coefficient by four to identify p.
3. For x²/100+y²/49=1, what is the full major-axis length?
Need a hint?
  • For an origin-centered ellipse with positive squared denominators, the larger denominator supplies the squared semi-major axis.
  • The denominator is a squared half-length, not the full axis length.
4. Find the vertices of x²/49−y²/64=1.
Need a hint?
  • An origin-centered horizontal hyperbola has a positive x² term and a subtracted y² term.
  • The positive squared term decides the transverse-axis direction.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Identify center and radius of (x−9)²+(y+10)²=81. Candidate answers: (A) Center (9,10); radius 9 (B) Center (9,−10); radius 81 (C) Center (9,−10); radius 9 (D) Center (−9,10); radius 9. 2. For x²=36y, find the focus. Candidate answers: (A) (0,36) (B) (0,9) (C) (0,−9) (D) (9,0). 3. For x²/144+y²/81=1, what is the full major-axis length? Candidate answers: (A) 12 units (B) 144 units (C) 18 units (D) 24 units. 4. Find the vertices of x²/81−y²/100=1. Candidate answers: (A) (0,−10) and (0,10) (B) (−10,0) and (10,0) (C) (−81,0) and (81,0) (D) (−9,0) and (9,0).

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. Center (9,−10); radius 9. Compare to (x−h)²+(y−k)²=r². Here h=9, k=−10, r=√81=9. The signs inside the parentheses are opposite the center coordinates. 2. (0,9). The standard vertical parabola form x²=4py has focus (0,p) and directrix y=−p. Thus p=36/4=9, and the focus is (0,9). 3. 24 units. The larger denominator is the square of the horizontal semi-major axis. Its half-length is 12; the full length is 2×12=24. 4. (−9,0) and (9,0). The positive x² term gives a horizontal transverse axis. Set y=0 to get x²/81=1, so x=±9.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.