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📅 Year 2024
Q1CBSE Board Exam 20243 Marks
Find the equation of the ellipse with foci (±4, 0) and length of major axis 12.
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Foci on x-axis ⇒ c = 4. Major axis 2a = 12 ⇒ a = 6.
b² = a² − c² = 36 − 16 = 20.
Centre at origin, so x²/36 + y²/20 = 1.
Q2CBSE Board Exam 20242 Marks
Find the equation of the parabola with focus (−2, 0) and directrix x = 2.
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Focus on negative x-axis, vertex at origin ⇒ y² = −4ax with a = 2.
y² = −8x.
📅 Year 2023
Q1CBSE Board Exam 20234 Marks
Find the equation of the hyperbola whose foci are (±3√5, 0) and the length of the latus rectum is 8.
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Foci (±3√5, 0) on x-axis ⇒ c = 3√5, so c² = 45.
Latus rectum = 2b²/a = 8 ⇒ b² = 4a.
Also c² = a² + b² ⇒ 45 = a² + 4a ⇒ a² + 4a − 45 = 0 ⇒ (a + 9)(a − 5) = 0 ⇒ a = 5 (a > 0).
b² = 4 × 5 = 20.
x²/25 − y²/20 = 1.