Q63.Let a circle ๐ถ touch the lines ๐ฟ1: 4๐ฅ- 3๐ฆ+ ๐พ1 = 0 and ๐ฟ2: 4๐ฅ- 3๐ฆ+ ๐พ2 = 0, ๐พ1, ๐พ2 โ๐ . If a line passing through the centre of the circle ๐ถ intersects ๐ฟ1 at -1, 2 and ๐ฟ2 at 3, - 6, then the equation of the circle ๐ถ is (1) ๐ฅ- 12 + ๐ฆ- 22 = 4 (2) ๐ฅ- 12 + ๐ฆ+ 22 = 16 (3) ๐ฅ+ 12 + ๐ฆ- 22 = 4 (4) ๐ฅ- 12 + ๐ฆ- 22 = 16
What This Question Tests
This question tests the ability to determine the center and radius of a circle given two parallel tangents and a line passing through its center, requiring calculations involving distance formulas and midpoint.
Concepts Tested
Formulas Used
Distance between parallel lines = |C1-C2|/sqrt(A^2+B^2)
Midpoint formula: ((x1+x2)/2, (y1+y2)/2)
Equation of a circle: (x-h)^2 + (y-k)^2 = r^2
Equation of a line: y-y1 = m(x-x1)
๐ NCERT Sections This Tests
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๐ Question Details
- Chapter
- Circles
- Topic
- Equation of a circle, distance between parallel lines
- Year
- 2022
- Shift
- 25 Jun Shift 1
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines; Class 11 Mathematics Ch 11: Conic Sections
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