Q65.If ๐ฅ2 - ๐ฆ2 + 2โ๐ฅ๐ฆ+ 2๐๐ฅ+ 2๐๐ฆ+ ๐= 0 is the locus of a point, which moves such that it is always equidistant from the lines ๐ฅ+ 2๐ฆ+ 7 = 0 and 2๐ฅ- ๐ฆ+ 8 = 0, then the value of ๐+ ๐+ โ- ๐ equals (1) 14 (2) 6 (3) 8 (4) 29
What This Question Tests
This question tests the ability to find the locus of a point equidistant from two lines, which represents the angle bisectors, and then compare it with a general conic equation to determine coefficients.
Concepts Tested
Formulas Used
Distance from (x1, y1) to Ax+By+C=0 is |Ax1+By1+C|/โ(Aยฒ+Bยฒ)
Equation of bisectors: (L1/|L1|) = ยฑ (L2/|L2|)
๐ NCERT Sections This Tests
2.1 โ Two Charges 5 ร 10โ8 C And โ3 ร 10โ8 C Are Located 16 Cm Apart. At
Physics Class 11 ยท Chapter 2
2.1 Two charges 5 ร 10โ8 C and โ3 ร 10โ8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
2.3 โ Two Charges 2 Mc And โ2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 ยท Chapter 2
2.3 Two charges 2 mC and โ2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
9.8 โ A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 ยท Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
๐ Question Details
- Chapter
- Straight Lines
- Topic
- Locus of a point, Angle bisectors
- Year
- 2024
- Shift
- 30 Jan Shift 2
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
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