#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

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  $\dpi{100} \Rightarrow$ y2 = 4. 6x/4 $\dpi{100} \Rightarrow$ 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)
$\dpi{80} \because$ It passes through (3/2,5), i.e., (3/2,5) satisfies eq. (1)
$\dpi{80} \therefore$ 5 = 3m/2 + 3/2m  $\dpi{100} \Rightarrow$ 5 = (3/2)(m + 1/m)
$\dpi{100} \Rightarrow$ 10/3 = (m2 + 1)/m
Solving above equation, we get
3m2 – 10m +3 = 0
$\dpi{100} \Rightarrow$ (3m – 1)(m – 3) = 0
m = 1/3   or   m = 3
Thus, the required slopes are 1/3 and 3.