Q70.The line x = 8 is the directrix of the ellipse E : x2 + y2 = 1 with the corresponding focus (2, 0). If the a2 b2 x -axis at tangent to E at the point P in the first quadrant passes through the point (0, 4√3) and intersects the Q, then (3PQ)2 is equal to _____ .
What This Question Tests
This multi-step question requires first finding the equation of the ellipse using its focus and directrix, then determining the point of tangency, finding the equation of the tangent, and finally calculating distances to solve for the required value.
Concepts Tested
Formulas Used
x²/a² + y²/b² = 1
e = a/d
Equation of tangent to ellipse at (x₁, y₁) is xx₁/a² + yy₁/b² = 1
📚 NCERT Sections This Tests
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1.18 — A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 · Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
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?
📋 Question Details
- Chapter
- Ellipse
- Topic
- Equation of ellipse, Tangent to ellipse
- Year
- 2023
- Shift
- 01 Feb Shift 2
- Q Number
- Q70
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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