Q67.Consider a hyperbola H : x2 −2y2 = 4 . Let the tangent at a point P(4, √6) meet the rectum at R(x1, y1), x1 > 0 . If F is a focus of H which is nearer to the point P , then the area of ΔQFR (in sq. units) is equal to (1) 4√6 (2) √6 −1 (3) 7 −2 (4) 4√6 −1 √6
What This Question Tests
This question tests the ability to find the equation of a tangent, intersect it with the latus rectum, identify the focus of a hyperbola, and calculate the area of a triangle formed by these points.
Concepts Tested
Formulas Used
xx_1/a^2 - yy_1/b^2 = 1
x = ae
Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
📚 NCERT Sections This Tests
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · 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.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
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
- Hyperbola
- Topic
- Tangent and Latus Rectum
- Year
- 2021
- Shift
- 18 Mar Shift 2
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q96.For the hyperbola = 1 , which of the following remains constant when α varies? cos2 α α − sin2 (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci
Q71.If the eccentricity of a hyperbola x2 K 2 is = 1, which passes through (K, 2), is √133 , then the value of 9 −y2b2 (1) 18 (2) 8 (3) 1 (4) 2
Q71.A tangent to the hyperbola x2 meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such 4 −y22 = 1 that OPRQ is a rectangle (where O is the origin). Then R lies on : (1) 4 + 2 = 1 (2) 2 − 4 = 1 x2 y2 x2 y2 (3) 2 + 4 = 1 (4) 4 − 2 = 1 x2 y2 x2 y2
Q72.Let P(3 sec θ, 2 tan θ) and Q(3 sec ϕ, 2 tan ϕ) where θ + ϕ = π2 , be two distinct points on the hyperbola x2 . Then the ordinate of the point of intersection of the normals at P and Q is: 9 −y24 = 1 (1) 11 3 (2) −113 (3) 13 2 (4) −132 = 5, then k is equal to: