Q71.Let ๐ be the point of intersection of the common tangents to the parabola ๐ฆ2 = 12๐ฅ and the hyperbola 8๐ฅ2 - ๐ฆ2 = 8. If ๐ and ๐' denote the foci of the hyperbola where ๐ lies on the positive ๐ฅ-axis then ๐ divides ๐๐' in a ratio: (1) 5: 4 (2) 2: 1 (3) 13: 11 (4) 14: 13
What This Question Tests
This question integrates concepts of tangents to both parabola and hyperbola, finding their common tangent, locating the intersection point, and then using the section formula to determine how this point divides the line segment joining the foci of the hyperbola.
Concepts Tested
Formulas Used
Equation of tangent to yยฒ=4ax is y=mx+a/m
Equation of tangent to xยฒ/aยฒ - yยฒ/bยฒ = 1 is y=mx ยฑ sqrt(aยฒmยฒ-bยฒ)
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.
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?
14.2 โ Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 ยท Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
๐ Question Details
- Chapter
- Parabola
- Topic
- Common tangents of conic sections
- Year
- 2019
- Shift
- 12 Apr Shift 1
- Q Number
- Q71
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
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