The largest and the shortest distance of the earth from sun are a and b, respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on the major axis meets the orbit is

\frac{a b}{a + b}

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\frac{a b}{2 (a + b)}

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\frac{2 a b}{a + b}

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\frac{a + b}{2 a b}

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Solution

The correct option is D $\frac{2 a b}{a + b}$
$\frac{y}{r} = 1 - e c o s θ$ (here $e$ is the eccentricity)
At $r = a$ , $θ = 0$
or
$\frac{y}{a} = 1 - e$
At $r = b$ $θ = 180^{o}$
or
$\frac{y}{b} = 1 + e$
Thus
$\frac{y}{a} + \frac{y}{b} = 2$
or
$y = \frac{2 a b}{a + b}$

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The largest and the shortest distance of the earth from sun are a and b, respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on the major axis meets the orbit is

The correct option is D 2aba+byr=1−ecosθ (here e is the eccentricity)At r=a, θ=0orya=1−eAt r=b θ=180ooryb=1+eThusya+yb=2ory=2aba+b

The correct option is D $\frac{2 a b}{a + b}$
$\frac{y}{r} = 1 - e c o s θ$ (here $e$ is the eccentricity)
At $r = a$ , $θ = 0$
or
$\frac{y}{a} = 1 - e$
At $r = b$ $θ = 180^{o}$
or
$\frac{y}{b} = 1 + e$
Thus
$\frac{y}{a} + \frac{y}{b} = 2$
or
$y = \frac{2 a b}{a + b}$