Q86.Let a common tangent to the curves ๐ฆ2 = 4๐ฅ and ๐ฅ- 42 + ๐ฆ2 = 16 touch the curves at the points ๐ and ๐. Then ๐๐2 is equal to ________.
What This Question Tests
This question involves finding the common tangent to a parabola and a circle, then determining the points of tangency and the squared distance between them, which requires simultaneous application of properties of both conic sections.
Concepts Tested
Formulas Used
y = mx + a/m (tangent to y^2=4ax)
(x-h)^2 + (y-k)^2 = r^2
Distance between two points
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.
2.2 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.
9.23 โ (A) At What Distance Should The Lens Be Held From The Card Sheet In
Physics Class 12 ยท Chapter 9
9.23 (a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum possible magnifying power? (b) What is the magnification in this case? (c) Is the magnification equal to the magnifying power in this case? Explain.
๐ Question Details
- Chapter
- Coordinate Geometry
- Topic
- Common tangent to curves
- Year
- 2023
- Shift
- 10 Apr Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections; Class 11 Mathematics Ch 10: Straight Lines
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Q76.If two vertices of an equilateral triangle are A(โa, 0) and B(a, 0), a > 0, and the third vertex C lies above x- axis then the equation of the circumcircle of โณABC is : (1) 3x2 + 3y2 โ2โ3ay = 3a2 (2) 3x2 + 3y2 โ2ay = 3a2 (3) x2 + y2 โ2ay = a2 (4) x2 + y2 โโ3ay = a2