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please answer fast..............slope of two tangent drawn from (3/2, 5) to parabola y^2=6x are??? please give solution

please answer fast..............slope of two tangent drawn from (3/2, 5) to parabola y^2=6x are???
please give solution

Grade:12

2 Answers

Shiva Rao
28 Points
2 years ago
 Since we know that
Slope =dy/dx
              =6x/2y
Now substitute the given Co ordinates
X=3/2 
Y=5
            =6×3/2×5×2
              =9/10
Samyak Jain
333 Points
2 years ago
y2 = 6x  \Rightarrow y2 = 4. 6x/4 \Rightarrow y2 = 4.(3/2)x
Comparing above equation with general equation of parabola y2 = 4ax, we get
a = 3/2
We know that equation of any tangent to parabola y2 = 4ax is
y = mx + a/m , where m is the slope of the tangent.
Here, equation of tangent would be y = mx + (3/2)/m   
i.e.              y = mx + 3/2m                                     ….(1)
\because It passes through (3/2,5), i.e., (3/2,5) satisfies eq. (1)
\therefore 5 = 3m/2 + 3/2m  \Rightarrow 5 = (3/2)(m + 1/m)
\Rightarrow 10/3 = (m2 + 1)/m
Solving above equation, we get
3m2 – 10m +3 = 0
\Rightarrow (3m – 1)(m – 3) = 0
m = 1/3   or   m = 3
Thus, the required slopes are 1/3 and 3.

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