The eccentricity of the conic represented by -x-22-y2-x-22-y2-8 is

The correct option is D 1/2 This #160;is #160;of #160;the #160;form #160; SP + SP^' = 2a ∴ PP^' = 2ae =√((2+2)^2) = 4 ...

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Standard XII

Mathematics

Eccentricity

The eccentric...

Question

The eccentricity of the conic represented by $\sqrt{(x + 2)^{2} + y^{2}} + \sqrt{(x - 2)^{2} + y^{2}} = 8$ is

\frac{1}{3}

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\frac{1}{2}

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\frac{1}{4}

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\frac{1}{5}

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Solution

The correct option is D $\frac{1}{2}$
This is of the form $S P + S P^{^{'}} = 2 a$
$∴ P P^{^{'}} = 2 a e$
$= \sqrt{(2 + 2)^{2}}$
$= 4$
$2 a e = 4$
But $2 a = 8$ (from the equation given)
$∴ e = \frac{1}{2}$

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The eccentricity of the conic represented by √(x+2)2+y2+√(x−2)2+y2=8 is

The correct option is D 12This is of the form SP+SP′=2a∴PP′=2ae=√(2+2)2=42ae=4But 2a=8 (from the equation given)∴e=12

The eccentricity of the conic represented by $\sqrt{(x + 2)^{2} + y^{2}} + \sqrt{(x - 2)^{2} + y^{2}} = 8$ is

The correct option is D $\frac{1}{2}$
This is of the form $S P + S P^{^{'}} = 2 a$
$∴ P P^{^{'}} = 2 a e$
$= \sqrt{(2 + 2)^{2}}$
$= 4$
$2 a e = 4$
But $2 a = 8$ (from the equation given)
$∴ e = \frac{1}{2}$