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  • tangents are drawn from the point (-8,0) to the parabola y^2=8x touch the parabola at P and Q.if F is the focus of the parabola then the area

tangents are drawn from the point (-8,0) to the parabola y^2=8x touch the parabola at P and Q.if F is the focus of the parabola then the area

Answers (1)

SUPPOSE y=mx+c IS THE EQUATION OF TANGENT TO PARABOLA FROM THE POINT (-8,0) THEN EQUATION WILL SATISFY (-8,0),SO WE WILL GET

0= (-8)m+c

8m=c               _eq(1)

NOW,IF y=mx+c IS EQUATION TO GIVEN PARABOLA THEN ,  mc=2     _eq(2)    

FROM eq(1) AND eq(2) WE WILL GET

m=+1/2, -1/2

THEN PUT VALUE OF m IN eq(1) WE WILL GET

c= +4 , -4

SO REQUIRED EQUATIONS OF TANGENTS WILL BE

 y = (1/2)x + 4    AND    y = (-1/2)x  - 4

NOW SOLVE THESE TWO EQUATIONS WITH PARABOLA TO GET POINT OF CONTACT RESPECTIVELY

ON SOLVING WE WILL GET,

P(8,8)   AND  Q(8,-8)  

NOW WE HAVE TO FIND AREA OF TRIANGLE FORMED BY POINTS (-8,0), (8,8), (-8,0) 

NOW DRAW THIS TRIANGLE ON CARTESIAN PLANE THEN APPLY FORMULA FOR AREA OF TRIANGLE THAT IS (1/2)*base*height

WE CAN SEE ON PLAN THAT HEIGHT OF TRIANGLE  = 16 units AND  BASE OF TRIANGLE =16 units

REQUIRED AREA OF TRIANGLE = (1/2)*(16)*(16) = 128 Sq units.

 

Posted by

arun shelke

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