Q72.If tangents are drawn to the ellipse x2 + 2y2 = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve : y2 (1) 1 + 1 = 1 (2) x2 4x2 2y2 4 + 2 = 1 y2 (3) 1 + 1 = 1 (4) x2 2x2 4y2 2 + 4 = 1
What This Question Tests
This question involves finding the equation of a tangent to an ellipse, determining its intercepts with the coordinate axes, finding the midpoint of the intercepted segment, and then eliminating the point of tangency to find the locus of the midpoint.
Concepts Tested
Formulas Used
Equation of tangent to x²/a²+y²/b²=1 at (x₁,y₁) is xx₁/a²+yy₁/b²=1
Midpoint formula ( (x₁+x₂)/2, (y₁+y₂)/2 )
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 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 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · 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?
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
📋 Question Details
- Chapter
- Ellipses
- Topic
- Tangent to an ellipse and locus
- Year
- 2019
- Shift
- 11 Jan Shift 1
- Q Number
- Q72
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q69.The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is (1) x2 + 16y2 = 16 (2) x2 + 12y2 = 16 (3) 4x2 + 48y2 = 48 (4) 4x2 + 64y2 = 48
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