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