This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Conic Sections – Parabola-1”.

1. Find the focus of parabola with equation y^{2}=100x.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

View Answer

Explanation: Comparing equation with y

^{2}=4ax.

4a=100 => a=25.

Focus is at (a, 0) i.e. (25, 0).

2. Find the focus of parabola with equation y^{2}=-100x.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

View Answer

Explanation: Comparing equation with y

^{2}=-4ax.

4a=100 => a=25.

Focus is at (-a, 0) i.e. (-25, 0).

3. Find the focus of parabola with equation x^{2}=100y.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

View Answer

Explanation: Comparing equation with x

^{2}=4ay.

4a=100 => a=25.

Focus is at (0, a) i.e. (0, 25).

4. Find the focus of parabola with equation x^{2}=-100y.

a) (0, 25)

b) (0, -25)

c) (25, 0)

d) (-25, 0)

View Answer

Explanation: Comparing equation with x

^{2}=-4ay.

4a=100 => a=25.

Focus is at (0, -a) i.e. (0, -25).

5. Find the equation of latus rectum of parabola y^{2}=100x.

a) x=25

b) x=-25

c) y=25

d) y=-25

View Answer

Explanation: Comparing equation with y

^{2}=4ax.

4a=100 => a=25. Line passing through focus perpendicular to axis is latus rectum.

Equation of latus rectum is x=a => x=25.

6. Find the equation of latus rectum of parabola y^{2}=-100x.

a) x=25

b) x=-25

c) y=-25

d) y=25

View Answer

Explanation: Comparing equation with y

^{2}=-4ax.

4a=100 => a=25. Line passing through focus perpendicular to axis is latus rectum.

Equation of latus rectum is x=-a => x=-25.

7. Find the equation of latus rectum of parabola x^{2}=100y.

a) x=25

b) x=-25

c) y=-25

d) y=25

View Answer

Explanation: Comparing equation with x

^{2}=4ay.

4a=100 => a=25. Line passing through focus perpendicular to axis is latus rectum.

Equation of latus rectum is y=a => y=25.

8. Find the equation of latus rectum of parabola x^{2}=-100y.

a) x=25

b) x=-25

c) y=-25

d) y=25

View Answer

Explanation: Comparing equation with x

^{2}=-4ay.

4a=100 => a=25. Line passing through focus perpendicular to axis is latus rectum.

Equation of latus rectum is y=-a => y=-25.

9. Find the equation of directrix of parabola y^{2}=100x.

a) x=25

b) x=-25

c) y=25

d) y=-25

View Answer

Explanation: Comparing equation with y

^{2}=4ax.

4a=100 => a=25. Directrix is a line parallel to latus rectum in such a way that vertex is at middle of both.

Equation of directrix is x=-a => x=-25.

10. Find the equation of directrix of parabola y^{2}=-100x.

a) x=25

b) x=-25

c) y=-25

d) y=25

View Answer

Explanation: Comparing equation with y

^{2}=-4ax.

4a=100 => a=25. Directrix is a line parallel to latus rectum in such a way that vertex is at middle of both.

Equation of directrix is x=a => x=25.

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