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If the line x+y-1=0 is a tangent to a parabola with focus (1,2) at A and intersects the diretrix at B and tangent at vertex at C,respectively. Then AC*BC is equal to?

AC denotes the length between the points A and C

Note by Rahul Chandani
2 years, 8 months ago

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In any parabola part of tangent between point of contact and directrix subtends right angle at focus.Also foot of perpendicular from focus on any tangent lies on tangent at vertex.Using these two facts we obtain that triangle ASB is right angled and that SC is perpendicular to AB.Using extension of Pythagoras theorem we have AC.BC=square of SC.We can easily calculate SC which is sqrt(2).Hence the answer is 2 Indraneel Mukhopadhyaya · 2 years ago

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