Q70.If the normal to the ellipse 3𝑥2 + 4𝑦2 = 12 at a point 𝑃 on it is parallel to the line, 2𝑥+ 𝑦= 4 and the tangent to the ellipse at 𝑃 passes through 𝑄( 4,4 ) then 𝑃𝑄 is equal to: (1) √61 (2) 5√5 2 2 (3) √157 (4) √221 2 2
What This Question Tests
This question is multi-step, involving finding a point on the ellipse using properties of its normal, then finding the equation of the tangent at that point, and finally calculating the distance between two points.
Concepts Tested
Formulas Used
Equation of normal to x²/a² + y²/b² = 1 at (x₁,y₁) is a²x/x₁ - b²y/y₁ = a²-b²
Slope of tangent at (x₁,y₁) is -(b²x₁)/(a²y₁)
📚 NCERT Sections This Tests
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?
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?
2.1 — 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.
📋 Question Details
- Chapter
- Ellipses
- Topic
- Tangents and Normals to Ellipse
- Year
- 2019
- Shift
- 12 Apr Shift 1
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
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