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प्रश्न
Find the coordinates of a point on the parabola y2 = 8x whose focal distance is 4.
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उत्तर
Given parabola is y2 = 8x ......(i)
Comparing with the equation of parabola y2 = 4ax
4a = 8
⇒ a = 2
Now focal distance = |x + a|
⇒ |x + a| = 4
⇒ (x + a) = ± 4
⇒ x + 2 = ± 4
⇒ x = 4 – 2 = 2
And x = – 6
But x ≠ – 6
∴ x = 2
Put x = 2 in equation (i) we get
y2 = 8 × 2 = 16
∴ y = ± 4
So, the coordinates of the point are (2, 4), (2, – 4).
Hence, the required coordinates are (2, 4) and (2, – 4).
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