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Maths-

General

Easy

Question

If two tangents drawn from the point ( $alpha comma beta$ ) to the parabola y² = 4x be such that the slope of one tangent is double of the other then

$β$ = $\frac{2}{9} α$ ²
$α$ = $\frac{2}{9} β$ ²
2 $α$ = 9 $β$ ²
none of these

The correct answer is: $alpha$ = $fraction numerator 2 over denominator 9 end fraction blank beta$ ²

To find the relation between $alpha comma beta$
$y equals m x plus alpha over m T a n g e n t space p a s s e s space t h r o u g h left parenthesis alpha comma beta right parenthesis space i s space beta equals m alpha plus space 1 divided by space m alpha m squared minus beta m plus 1 divided by m equals 0 m subscript 1 equals m comma space m subscript 2 equals 2 m m plus 2 m equals beta over alpha m equals fraction numerator beta over denominator 3 alpha end fraction 2 m x m equals 1 divided by alpha 2 open parentheses fraction numerator beta squared over denominator 3 alpha end fraction close parentheses equals 1 divided by alpha beta equals 3 square root of alpha over 2 end root alpha equals fraction numerator 2 beta squared over denominator 9 end fraction$

Therefore, $alpha$ = $fraction numerator 2 over denominator 9 end fraction blank beta$ 2.

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