Grade 12Analytical Geometry

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

Mrunal Sonawane

7 Years agoGrade 12

2 Answers

Shiva Rao

7 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

Approved Tutor Answer7 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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please answer fast..............slope of two tangent drawn from (3/2, 5) to parabola y^2=6x are???please give solution

Mrunal Sonawane

2 Answers

Shiva Rao

Samyak Jain

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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