10.1 circle and system of circle - Gujarat Board (GSEB) STD 11 Science MATHS Questions - Vidyadip

Question types

10.1 circle and system of circle question types

738 questions across 1 question group — pick any mix to generate a MATHS paper with step-by-step answer keys.

738

Questions

1

Question groups

5

Question types

MCQ

Sample Questions

10.1 circle and system of 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 equation of the circle passing through the point $( - 1,\; - 3)$ and touching the line $4x + 3y - 12 = 0$ at the point $(3, 0)$ is

✓
${x^2} + {y^2} - 2x + 3y - 3 = 0$
B
${x^2} + {y^2} + 2x - 3y - 5 = 0$
C
$2{x^2} + 2{y^2} - 2x + 5y - 8 = 0$
D
None of these

Answer: A.

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Q 2MCQ1 Mark

If the vertices of a triangle be $(2,\; - 2)$, $( - 1,\; - 1)$ and $(5, 2)$, then the equation of its circumcircle is

A
${x^2} + {y^2} + 3x + 3y + 8 = 0$
✓
${x^2} + {y^2} - 3x - 3y - 8 = 0$
C
${x^2} + {y^2} - 3x + 3y + 8 = 0$
D
None of these

Answer: B.

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Q 3MCQ1 Mark

The equation of a circle which touches both axes and the line $3x - 4y + 8 = 0$ and whose centre lies in the third quadrant is

A
${x^2} + {y^2} - 4x + 4y - 4 = 0$
B
${x^2} + {y^2} - 4x + 4y + 4 = 0$
✓
${x^2} + {y^2} + 4x + 4y + 4 = 0$
D
${x^2} + {y^2} - 4x - 4y - 4 = 0$

Answer: C.

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Q 4MCQ1 Mark

The equation of the circle passing through the origin and cutting intercepts of length $3$ and $4$ units from the positive axes, is

A
${x^2} + {y^2} + 6x + 8y + 1 = 0$
B
${x^2} + {y^2} - 6x - 8y = 0$
C
${x^2} + {y^2} + 3x + 4y = 0$
✓
${x^2} + {y^2} - 3x - 4y = 0$

Answer: D.

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Q 5MCQ1 Mark

Equation of the circle which touches the lines $x = 0,\;y = 0$ and $3x + 4y = 4$ is

A
${x^2} - 4x + {y^2} + 4y + 4 = 0$
✓
${x^2} - 4x + {y^2} - 4y + 4 = 0$
C
${x^2} + 4x + {y^2} + 4y + 4 = 0$
D
${x^2} + 4x + {y^2} - 4y + 4 = 0$

Answer: B.

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