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Botany-

General

Easy

Question

Tangent at any point of ellipse $9 x to the power of 2 end exponent plus 16 y to the power of 2 end exponent minus 144 equals 0$ is drawn. Eccentric
angle of ‘ P’ is $theta equals fraction numerator 1 over denominator 2 end fraction s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 7 end fraction close parentheses$ If is the foot of perpendicular from centre $blank ´ O blank ´$ to this tangent then $angle P O N$ is

${t a n}^{- 1} (\frac{1}{12})$
${t a n}^{- 1} (\frac{1}{24})$
$\frac{π}{12}$
$\frac{π}{3}$

The correct answer is:
$t a n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 24 end fraction close parentheses$

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If the curve $x to the power of 2 end exponent plus 3 y to the power of 2 end exponent equals 9$ subtends as obtuse angle at the point $left parenthesis 2 alpha comma alpha right parenthesis left parenthesis left parenthesis alpha element of text int end text text eger end text text end text right parenthesis$ , $blank left parenthesis alpha element of text int eger end text right parenthesis$ then a possible value of 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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