The largest and the shortest distance of the earth from the sun are $r_{1}$ and $r_{2}$ . Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is:

\frac{r_{1} + r_{2}}{4}

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\frac{r_{1} + r_{2}}{r_{1} - r_{2}}

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\frac{2 r_{1} r_{2}}{r_{1} + r_{2}}

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\frac{r_{1} + r_{2}}{3}

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Solution

The correct option is C $\frac{2 r_{1} r_{2}}{r_{1} + r_{2}}$
From the property of ellipse
$\frac{2}{R} = \frac{1}{r_{1}} + \frac{1}{r_{2}}$
$\frac{2}{R} = \frac{r_{1} + r_{2}}{r_{1} r_{2}}$
$R = \frac{2 r_{1} r_{2}}{r_{1} + r_{2}}$

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The largest and the shortest distance of the earth from the sun are $r_{1}$ and $r_{2}$ , its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun

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R_{1}

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are the maximum ranges of a projectile when it is projected from the bottom and top respectively of an inclined plane respectively, then find the maximum range of the projectile when it is projected from the ground with same velocity.

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Cases Conditions

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t. 5. $r_{1} + r_{2} = c_{1} r_{2}$

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The largest and the shortest distance of the earth from the sun are r1 and r2. Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is:

The correct option is C 2r1r2r1+r2From the property of ellipse2R=1r1+1r22R=r1+r2r1r2R=2r1r2r1+r2

The largest and the shortest distance of the earth from the sun are $r_{1}$ and $r_{2}$ . Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun is:

The correct option is C $\frac{2 r_{1} r_{2}}{r_{1} + r_{2}}$
From the property of ellipse
$\frac{2}{R} = \frac{1}{r_{1}} + \frac{1}{r_{2}}$
$\frac{2}{R} = \frac{r_{1} + r_{2}}{r_{1} r_{2}}$
$R = \frac{2 r_{1} r_{2}}{r_{1} + r_{2}}$