Tangents are drawn from (-1,0) to y^2=4x.then the area of the triangle formed by the tangents and the chord of the contact is:
 
1)8sq. Units    2)2sq. Units    3)4 sq. Units   4)1 sq. Units

Asked by Sunil Soni | 17th Oct, 2015, 09:25: AM

Expert Answer:

begin mathsize 11px style Equation space of space chord space of space contact space from space left parenthesis straight x subscript 1 comma space straight y subscript 1 right parenthesis space to space straight y squared equals 4 straight x space is yy subscript 1 equals 2 open parentheses straight x plus straight x subscript 1 close parentheses So comma space equation space of space chord space of space contact space from space left parenthesis negative 1 comma space 0 right parenthesis space is space straight y cross times 0 equals 2 open parentheses straight x minus 1 close parentheses rightwards double arrow straight x equals 1 Substituting space straight x equals 1 space in space the space equation space straight y squared equals 4 straight x comma space we space get straight y equals plus-or-minus 2. Hence comma space the space coordinates space of space vertices space of space the space triangle space are straight P open parentheses negative 1 comma 0 close parentheses comma space straight Q open parentheses 1 comma space 2 close parentheses space and space straight R open parentheses 1 comma space minus 2 close parentheses. QR equals 4 Length space of space perpendicular space from space straight P space to space QR space is space 2. Hence comma space area space equals space 1 half cross times 4 cross times 2 equals space 4 space sq space units. 3 rd space option space is space correct. end style

Answered by satyajit samal | 18th Oct, 2015, 07:09: AM