Question

Equation of the parabola with its vertex at (1, 1)and focus

(3, 1)is

• A. $(x - 1)^{2} = 8(y - 1)$
• B. $(y - 1)^{2} = 8(x - 3)$
• C. $(y - 1)^{2} = 8(x - 1)$
• D. $(x - 3)^{2} = 8(y - 1)$

Answer 1

Answer: (C)

$(y - 1)^{2} = 8(x - 1)$

Answer 2

Given vertex of parabola $(h,k) \equiv (1,1)$ and its focus

$(a + h,k) \equiv (3,1)$ or $a + h = 3$or $a = 2$. We know that as the y- coordinates of vertex and focus are same, therefore axis of parabola is parallel to x-axis. Thus equation of the parabola is $\mathbf{(y - k}\mathbf{)}^{\mathbf{2}}\mathbf{= 4a(x - h)}$ or $(y - 1)^{2} = 4 \times 2(x - 1)$ or

$(y - 1)^{2} = 8(x - 1)$