If focal distance of a point on the parabola y = x 2 − 4 is 4 25 and points are of the form ( ± a , b ) Then a + b is equal to

y + 4 = x 2 x 2 = 4. 4 1 ( y + 4 ) Focal distance = 4 25 Distance from directrix ( y = 4 − 15 ) Ordinate of points on the parabola whose focal distance is 4 25 = 4 − 17 + 4 25 = 2 points are ( ± 6 , 2 ) ⇒ a + b = 8

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MathematicsParabolaGeneralMedium2 minQB

MathematicsMediumsingle choice

If focal distance of a point on the parabola $y = x^{2} - 4$ is $\frac{25}{4}$ and points are of the form $(\pm a, b)$ Then $a + b$ is equal to

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Answer:

Solution:

$y + 4 = x^{2}$

$x^{2} = 4. \frac{1}{4} (y + 4)$

Focal distance $= \frac{25}{4}$

Distance from directrix $(y = \frac{- 15}{4})$
Ordinate of points on the parabola whose focal distance is $\frac{25}{4}$

$= \frac{- 17}{4} + \frac{25}{4} = 2$ points are $(\pm 6, 2) \Rightarrow a + b = 8$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:General

⏱ 2mℹ️ Source: QB

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