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Botany-

General

Easy

Question

Let $Q equals left parenthesis 3 comma square root of 5 right parenthesis comma R equals left parenthesis 73 square root of 5 right parenthesis$ . A point P in the XY-plane varies in such a way that perimeter of $capital delta P Q R$ is 16. Then the maximum area of $capital delta P Q R$ is

6
12
18
9

The correct answer is: 12

P lies on the ellipse for which are foci and length of major axis is 10 and eccentricity is 3/5.

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$P comma Q blank$ are points on the ellipse $fraction numerator x to the power of 2 end exponent over denominator 25 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 16 end fraction equals 1$ such that $P Q$ is a chord through the point $R left parenthesis 3 , 0 right parenthesis text . end text$ If $vertical line P R vertical line equals 2$ then length of chord $P Q$ is

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From the focus $left parenthesis negative 5 , 0 right parenthesis$ of the ellipse $fraction numerator x to the power of 2 end exponent over denominator 45 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 20 end fraction equals 1$ a ray of light is sent which makes angle $c o s to the power of negative 1 end exponent invisible function application open parentheses fraction numerator negative 1 over denominator square root of 5 end fraction close parentheses$ with the positive direction of X-axis upon reacting the ellipse the ray is reflected from it. Slope of the reflected ray is

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Physics-General

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