Question types

Circle question types

226 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

226
Questions
6
Question groups
5
Question types
Sample Questions

Circle 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
The parametric equations of the circle $x^2+y^2+m x+m y=0$ are
  • $x=\frac{-m}{2}+\frac{m}{\sqrt{2}} \cos \theta_i y=\frac{-m}{2}+\frac{m}{\sqrt{2}} \sin \theta$
  • B
    $x=\frac{-m}{2}+\frac{m}{\sqrt{2}} \cos \theta_2 y=\frac{+m}{2}+\frac{m}{\sqrt{2}} \sin \theta$
  • C
    x = 0, y = 0
  • D
    x = m cos θ, y = m sin θ

Answer: A.

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Q 2MCQ1 Mark
A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of 60. The area enclosed by these tangents and the arc of the circle is
  • A
    $\frac{2}{\sqrt{3}}-\frac{\pi}{6}$
  • $\sqrt{3}-\frac{\pi}{3}$
  • C
    $\frac{\pi}{3}-\frac{\sqrt{3}}{6}$
  • D
    $\sqrt{3}\left(1-\frac{\pi}{6}\right)$

Answer: B.

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Q 3MCQ1 Mark
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
  • A
    $x^2+y^2=9 a^2$
  • B
    $x^2+y^2=16 a^2$
  • $x^2+y^2=4 a^2$
  • D
    $x^2+y^2=a^2$

Answer: C.

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Q 4MCQ1 Mark
If a circle passes through the points (0, 0), (a, 0), and (0, b), then find the co-ordinates of its centre.
  • A
    $\left(\frac{-a}{2}, \frac{-b}{2}\right)$
  • B
    $\left(\frac{a}{2}, \frac{-b}{2}\right)$
  • C
    $\left(\frac{-a}{2}, \frac{b}{2}\right)$
  • $\left(\frac{a}{2}, \frac{b}{2}\right)$

Answer: D.

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Q 5MCQ1 Mark
The area of the circle having centre at (1, 2) and passing through (4, 6) is
  • A
  • B
    10π
  • 25π
  • D
    100π

Answer: C.

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Tangents to the circle $x^2+y^2=a^2$ with inclinations, $\theta_1$ and $\theta_2$ intersect in $P$. Find the locus of P such that

1.$\tan \theta_1+\tan \theta_2=0$

2. $\cot \theta_1+\cot \theta_2=5$

3. $\cot \theta_1 \cdot \cot \theta_2=c$

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