Question types

CONIC SECTIONS question types

277 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

277
Questions
5
Question groups
5
Question types
Sample Questions

CONIC SECTIONS questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If the equation $\frac{\lambda(\text{x}+1)^2}{3}+\frac{(\text{y}+2)^2}{4}=1$ represents a circle then $\lambda$:
  • A
    $1$
  • $\frac{3}{4}$
  • C
    $0$
  • D
    $-\frac{3}{4}$

Answer: B.

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Q 2MCQ1 Mark
The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is:
  • $\frac{\sqrt{5}-1}{2}$
  • B
    $\frac{\sqrt{5}+1}{2}$
  • C
    $\frac{\sqrt{5}-1}{4}$
  • D
    $\text{none of these}$

Answer: A.

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Q 3MCQ1 Mark
Find the equation of the circle. Centered at (3, -2) with radius 4:
  • A
    $x^2+y^2+6 x-4 y=3$
  • $x^2+y^2-6 x+4 y=3$
  • C
    $x^2+y^2-3 x+2 y=-3$
  • D
    $x^2+y^2+3 x-2 y=-3$

Answer: B.

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Q 4MCQ1 Mark
The equation of ellipse whose one focus is at (4, 0) and whose eccentricity is $\frac{4}{5}$ is:
  • A
    $\frac{\text{x}^2}{5}+\frac{\text{y}^2}{9}=1$
  • $\frac{\text{x}^2}{25}+\frac{\text{y}^2}{9}=1$
  • C
    $\frac{\text{x}^2}{9}+\frac{\text{y}^2}{5}=1$
  • D
    $\frac{\text{x}^2}{9}+\frac{\text{y}^2}{25}=1$

Answer: B.

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Q 5MCQ1 Mark
The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 is:
 
  • A
    $x^2+y^2-6 x-6 y+9=0$
  • $4\left(x^2+y^2-x-y\right)+1=0$
  • C
    $4\left(x^2+y^2+x+y\right)+1=0$
  • D
    None of these

Answer: B.

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A man running a racecourse notes that the sum of the distances from the two flag posts from him is always $10 m$ and the distance between the flag posts is $8 m$. Find the equation of the path traced by the man.
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A rod of length $12 m$ moves with its ends always touching the coordinates axes. Determine the equation of the locus of a point P on the rod, which is $3 cm$ from the end in contact with the X-axis.
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The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100 m$ long is supported by vertical wires attached to the cable, the longest wire being $30 m$ and the shortest being $6 m$. Find the length of a supporting wire attached to the roadway $18 m$ from the middle.
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A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10m and the distance between the flag posts is 8m. Find the equation of the posts traced by the man.
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Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. $36x^2 + 4y^2 = 144$
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The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100m$ long is supported by vertical wires attached to the cable, the longest wire being $30m$ and the shortest being 6m. Find the length of a supporting wire attached to the roadway 18m from the middle.
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