Parabolas: focus, directrix and equations
Grade 11 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
Luz designs a lamp reflector with its focus at (2, 5) and its directrix y = 1. Which equation is the reflector's curve?
- (x − 2)² = 8(y − 3)
- (y − 3)² = 8(x − 2)
- (x + 2)² = 8(y + 3)
- (x − 2)² = 16(y − 3)
Milo marks the focus (5, -1) and the directrix x = 1 on graph paper. Which equation is the parabola?
- (x − 3)² = 8(y + 1)
- (y + 1)² = 8(x − 3)
- (y − 1)² = 8(x + 3)
- (y + 1)² = 16(x − 3)
Ren marks the focus (-6, 2) and the directrix x = 2 on graph paper. Which equation is the parabola?
- (y − 2)² = -32(x + 2)
- (y − 2)² = -16(x + 2)
- (y + 2)² = -16(x − 2)
- (x + 2)² = -16(y − 2)
Tala writes a parabola on graph paper as x² − 8x − 8y + 8 = 0. Which equation is the same curve in standard form?
- (x − 4)² = 8(y − 1)
- (x + 4)² = 8(y + 1)
- (x − 4)² = 8(y + 3)
- (x − 4)² = 8(y + 1)
Zee writes a lamp reflector's curve as y² + 12y − 12x + 48 = 0. Which equation is the same curve in standard form?
- (y + 6)² = 12(x − 1)
- (y + 6)² = 12(x + 7)
- (y − 6)² = 12(x − 1)
- (y + 6)² = 12(x − 4)
Esme writes a fountain's arc of water as x² + 4x + 4y − 8 = 0. Which equation is the same curve in standard form?
- (x + 2)² = -4(y − 3)
- (x − 2)² = -4(y − 3)
- (x + 2)² = -4(y − 2)
- (x + 2)² = -4(y + 1)
Jun writes a parabola on graph paper as y² − 8y + 8x + 24 = 0. Which equation is the same curve in standard form?
- (y − 4)² = -8(x + 3)
- (y + 4)² = -8(x + 1)
- (y − 4)² = -8(x + 1)
- (y − 4)² = -8(x − 5)
Luz writes a parabola on graph paper as y = (1/12)(x − 2)² + 3. Where is its focus?
Milo models a lamp reflector's curve as y = (1/8)(x + 1)² − 4. The bulb goes at the focus. Where is the focus?
Ren writes a parabola on graph paper as y = (1/4)(x + 5)² + 1. Where is its focus?