JEE Main 2019MathematicsHyperbolaQuestion Based On Basic Definition And Parametric RepresentationmediumMCQ
JEE Main 2019 — Hyperbola Question with Solution
From: JEE Main 2019 (Online) 10th April Morning Slot
Question
If a directrix of a hyperbola centred at the origin and passing through the point (4, –23 ) is 5x = 45 and
its eccentricity is e, then :
Choose an option
▸Show full solutionCorrect option: B
Correct answer
B4e4 – 24e2 + 35 = 0
Step-by-step explanation
5x = 45
⇒x=54
Equation of hyperbola
a2x2−b2y2=1 it passes through (4,−23)
∴e2=1+a2b2
⇒a2e2−a2=b2
⇒a216−a2e2−a212=1
⇒a24[14−e2−13]=1
⇒4e2−4−3=(e2−1)(4a2)
⇒4(4e3−7)=(e2−1)(54e)2
⇒4e4−24e2+35=0
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