Q70.Let A be a point on the x-axis. Common tangents are drawn from A to the curves x2 + y2 = 8 and y2 = 16x . If one of these tangents touches the two curves at Q and R, then (QR)2 is equal to (1) 64 (2) 76 (3) 81 (4) 72
What This Question Tests
This problem requires finding the common tangent to a circle and a parabola, determining the points of tangency, and then calculating the distance between these points, which is a multi-step process.
Concepts Tested
Formulas Used
Tangent to x^2+y^2=r^2: yy1 = x x1 + r^2
Tangent to y^2=4ax: y=mx+a/m
Distance formula
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?
2.2 โ A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 ยท Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
๐ Question Details
- Chapter
- Coordinate Geometry
- Topic
- Common Tangents to Circle and Parabola
- Year
- 2023
- Shift
- 30 Jan Shift 2
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (Parabola, Circle)
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