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# 1. the angle between the tangents drawn from the point (1,4)to the parabola y=4x is2. In what ratio is the line y-x+2=0 divides the line joining the point (3,-1) & (8,9)

## 1 Answers

10 years ago

Dear  rajan,

eqution of pair of tangent   SS1 = T2

12(Y2 - 4X)  =(4Y-2X-2)2

WE GET   4X2 +4Y2 -16XY - 40X-16Y+4 = 0

TANß = 2√H2-AB/A+B       ABOVE EQUTION H = -8 ,A = 4,B=4

AND PUTTING THE VALUES WE GET TANß = √3  ß = 60 AND 300

QUES 2

LET Xm , Ym  BE THE POINTS THAT LIES ON THE LINE and divides the line joining (3, -1) (8,9) in ratio m,n

Xm = (3m+8n)/(m+n)     Ym = (-m+9n)/(m+n)  AS THE POINTS LIE ON THE LINE SO

Ym-Xm+2=0

(3m+8n)/(m+n) -(-m+9n)/(m+n) = -2

taking n common

(3(m/n) + 8) /((m/n)+1) -(-(m/n) + 9) /((m/n)+1) = -2

take m/n as p

solving we get

p = 1/6  is the answer

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