Q70.If each of the lines 5x + 8y = 13 and 4x −y = 3 contains a diameter of the circle x2 + y2 −2 (a2 −7a + 11) x −2 (a2 −6a + 6)y + b3 + 1 = 0, then : (1) a = 5 and b ∉(−1, 1) (2) a = 1 and b ∉(−1, 1) (3) a = 2 and b ∉(−∞, 1) (4) a = 5 and b ∈(−∞, 1)
What This Question Tests
This question requires identifying the center of the given circle from its general equation and then using the fact that diameters of a circle must pass through its center, forming a system of linear equations to solve for 'a'.
Concepts Tested
Formulas Used
Equation of circle x²+y²+2gx+2fy+c=0
Center (-g,-f)
Diameter passes through center
📚 NCERT Sections This Tests
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5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
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4.8 A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
📋 Question Details
- Chapter
- Circles
- Topic
- Equation of a circle and its properties
- Year
- 2013
- Shift
- 09 Apr Online
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (specifically Circles)
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