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Maths-

General

Easy

Question

PSQ is a focal chord of a parabola whose focus is S & vertex A . PA and QA are produced to meet the directrix in R and T respectively then $straight angle RST equals$

90º
60º
45º
30º

The correct answer is: 90º

To find angle $straight angle RST equals$
Let parabola $y squared equals 4 a x$
Equation of TAQ = y = $open parentheses fraction numerator begin display style fraction numerator negative 2 a over denominator t end fraction end style over denominator begin display style a over t squared end style end fraction close parentheses x$
y=(-2t)x
At x=-a;
y=2at
T=(a,2at)
Equation of RAP is y= $open parentheses open parentheses fraction numerator 2 a t over denominator a t squared end fraction close parentheses close parentheses x$
$R equals open parentheses negative a comma fraction numerator negative 2 a over denominator t end fraction close parentheses S l o p e space o f space S T equals m 1 equals negative t S l o p e space o f space S R equals m 2 equals 1 over t tan left parenthesis R S T right parenthesis equals fraction numerator m 2 minus m 1 over denominator 1 plus m 1 m 2 end fraction equals 1 over 0 equals infinity angle R S T equals 90 degree$

Therefor angle $angle R S T equals 90 degree$

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