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JEE • MATHEMATICS • SYSTEM OF CIRCLES

System of circles practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 4

Analyzing +4 | -1

If the circle

{C_1}\;:{x^2} + {y^2} = 16

intersects another circle

{C_2}

of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to

3/4

, the coordinates of the centre of

{C_2}

are

View answer and explanation

Correct option: A

\left( { - 9/5,12/5} \right),\left( {9/5, - 12/5} \right)

Option D is correct because the condition for no solution is that the constant 'c' must be greater than a certain value derived from tangency.

2 Hard

2 of 4

Application +4 | -1

One of the limit point of the coaxial system of circles containing

{x^2} + {y^2} - 6\;x - 6\;y + 4 = 0,\;\;{x^2} + {y^2} - 2\;x - 4\;y + 3 = 0,

View answer and explanation

Correct option: A

\left( { - 1,1} \right)

Option A (

\left( { - 1,1} \right)

) is correct because it represents one of the limit points of the coaxial system of circles, found by setting the radius to zero.

3 Hard

3 of 4

Application +4 | -1

Origin is a limiting point of a coaxial system of which

{x^2} + {y^2} - 6x - 8y + 1 = 0

is a member. The other limiting point is

View answer and explanation

Correct option: B

\left( {3/25,4/25} \right)

Option B (

\left( {3/25,4/25} \right)

) is correct because it is calculated using the formula for limiting points of a coaxial system of circles.

4 Hard

4 of 4

Analyzing +4 | -1

The equation

{x^2} + {y^2} - 2x - 2\lambda \mathrm{ }y - 8 = 0

represents a system of circles,

\lambda

being a parameter, passing through two fixed points

P

and

Q

. The circle on

PQ

as a diameter, is

View answer and explanation

Correct option: B

{x^2} + {y^2} - 2x - 8 = 0

Option B (

{x^2} + {y^2} - 2x - 8 = 0

) is the correct equation of the circle on PQ as a diameter, found by setting

\lambda = 0

in the given equation.

Revision notes and key takeaways

Review SYSTEM OF CIRCLES in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 4 single-correct-answer MCQs on SYSTEM OF CIRCLES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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System of circles practice · Hard

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