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Hyperbola question

2020 · Shift 2 · Q26
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  2. /JEE Advanced
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  5. /2020 · Shift 2 · Q26

Hyperbola question

2020 · Shift 2 · Q26

JEE AdvancedMathematicsHyperbolaMultiple correct+4 / −2
Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola x2a2−y2b2=1{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1a2x2​−b2y2​=1. Suppose the tangent to the hyperbola at P passes through the point (1, 0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let Δ\DeltaΔ denote the area of the triangle formed by the tangent at P, the normal at P and the X-axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?
  1. A
    1<e<21 \lt e \lt \sqrt 21<e<2​
  2. B
    2<e<2\sqrt 2 \lt e \lt 22​<e<2
  3. C
    Δ=a4\Delta = {a^4}Δ=a4
  4. D
    Δ=b4\Delta = {b^4}Δ=b4
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